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bifurcation</title> <meta name="description" content="Search results for: Hopf bifurcation"> <meta name="keywords" content="Hopf bifurcation"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none 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publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">64</span> Hopf Bifurcation for a New Chaotic System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Kejun%20Zhuang">Kejun Zhuang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, a three dimensional autonomous chaotic system is considered. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived with the help of normal form theory. Finally, a numerical example is given.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Chaotic%20system" title="Chaotic system">Chaotic system</a>, <a href="https://publications.waset.org/search?q=Hopf%20bifurcation" title=" Hopf bifurcation"> Hopf bifurcation</a>, <a href="https://publications.waset.org/search?q=normal%20form%20theory." title=" normal form theory."> normal form theory.</a> </p> <a href="https://publications.waset.org/8801/hopf-bifurcation-for-a-new-chaotic-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/8801/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/8801/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/8801/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/8801/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/8801/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/8801/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/8801/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/8801/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/8801/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/8801/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/8801.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1446</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">63</span> Bifurcation Analysis in a Two-neuron System with Different Time Delays</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Changjin%20Xu">Changjin Xu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, we consider a two-neuron system with time-delayed connections between neurons. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation results are given to support the theoretical predictions. Finally, main conclusions are given.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Two-neuron%20system" title="Two-neuron system">Two-neuron system</a>, <a href="https://publications.waset.org/search?q=delay" title=" delay"> delay</a>, <a href="https://publications.waset.org/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/search?q=Hopf%20bifurcation." title=" Hopf bifurcation."> Hopf bifurcation.</a> </p> <a href="https://publications.waset.org/15407/bifurcation-analysis-in-a-two-neuron-system-with-different-time-delays" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/15407/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/15407/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/15407/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/15407/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/15407/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/15407/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/15407/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/15407/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/15407/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/15407/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/15407.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1325</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">62</span> Periodic Oscillations in a Delay Population Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Changjin%20Xu">Changjin Xu</a>, <a href="https://publications.waset.org/search?q=Peiluan%20Li"> Peiluan Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, a nonlinear delay population model is investigated. Choosing the delay as a bifurcation parameter, we demonstrate that Hopf bifurcation will occur when the delay exceeds a critical value. Global existence of bifurcating periodic solutions is established. Numerical simulations supporting the theoretical findings are included.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Population%20model" title="Population model">Population model</a>, <a href="https://publications.waset.org/search?q=Stability" title=" Stability"> Stability</a>, <a href="https://publications.waset.org/search?q=Hopf%20bifurcation" title=" Hopf bifurcation"> Hopf bifurcation</a>, <a href="https://publications.waset.org/search?q=Delay" title=" Delay"> Delay</a>, <a href="https://publications.waset.org/search?q=Global%20Hopf%20bifurcation." title=" Global Hopf bifurcation."> Global Hopf bifurcation.</a> </p> <a href="https://publications.waset.org/576/periodic-oscillations-in-a-delay-population-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/576/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/576/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/576/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/576/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/576/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/576/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/576/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/576/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/576/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/576/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/576.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1752</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">61</span> HOPF Bifurcation of a Predator-prey Model with Time Delay and Habitat Complexity</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Li%20Hongwei">Li Hongwei</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, a predator-prey model with time delay and habitat complexity is investigated. By analyzing the characteristic equations, the local stability of each feasible equilibria of the system is discussed and the existence of a Hopf bifurcation at the coexistence equilibrium is established. By choosing the sum of two delays as a bifurcation parameter, we show that Hopf bifurcations can occur as crosses some critical values. By deriving the equation describing the flow on the center manifold, we can determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main theoretical results.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Predator-prey%20system" title="Predator-prey system">Predator-prey system</a>, <a href="https://publications.waset.org/search?q=delay" title=" delay"> delay</a>, <a href="https://publications.waset.org/search?q=habitat%20complexity" title=" habitat complexity"> habitat complexity</a>, <a href="https://publications.waset.org/search?q=HOPF%20bifurcation." title=" HOPF bifurcation."> HOPF bifurcation.</a> </p> <a href="https://publications.waset.org/10173/hopf-bifurcation-of-a-predator-prey-model-with-time-delay-and-habitat-complexity" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10173/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10173/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10173/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10173/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10173/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10173/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10173/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10173/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10173/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10173/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10173.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1870</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">60</span> Frequency Domain Analysis for Hopf Bifurcation in a Delayed Competitive Web-site Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Changjin%20Xu">Changjin Xu</a>, <a href="https://publications.waset.org/search?q=Yusen%20Wu"> Yusen Wu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, applying frequency domain approach, a delayed competitive web-site system is investigated. By choosing the parameter α as a bifurcation parameter, it is found that Hopf bifurcation occurs as the bifurcation parameter α passes a critical values. That is, a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. Some numerical simulations are included to justify the theoretical analysis results. Finally, main conclusions are given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Web-site%20system" title="Web-site system">Web-site system</a>, <a href="https://publications.waset.org/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/search?q=Nyquist%20criterion" title=" Nyquist criterion"> Nyquist criterion</a>, <a href="https://publications.waset.org/search?q=Hopf%0D%0Abifurcation" title=" Hopf bifurcation"> Hopf bifurcation</a>, <a href="https://publications.waset.org/search?q=frequency%20domain." title=" frequency domain."> frequency domain.</a> </p> <a href="https://publications.waset.org/10004338/frequency-domain-analysis-for-hopf-bifurcation-in-a-delayed-competitive-web-site-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10004338/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10004338/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10004338/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10004338/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10004338/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10004338/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10004338/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10004338/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10004338/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10004338/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10004338.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1465</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">59</span> Bifurcation Analysis for a Physiological Control System with Delay</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Kejun%20Zhuang">Kejun Zhuang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, a delayed physiological control system is investigated. The sufficient conditions for stability of positive equilibrium and existence of local Hopf bifurcation are derived. Furthermore, global existence of periodic solutions is established by using the global Hopf bifurcation theory. Finally, numerical examples are given to support the theoretical analysis.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Physiological%20control%20system" title="Physiological control system">Physiological control system</a>, <a href="https://publications.waset.org/search?q=global%20Hopf%20bifurcation" title=" global Hopf bifurcation"> global Hopf bifurcation</a>, <a href="https://publications.waset.org/search?q=periodic%20solutions." title=" periodic solutions."> periodic solutions.</a> </p> <a href="https://publications.waset.org/2546/bifurcation-analysis-for-a-physiological-control-system-with-delay" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/2546/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/2546/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/2546/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/2546/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/2546/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/2546/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/2546/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/2546/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/2546/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/2546/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/2546.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1558</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">58</span> Stability and Bifurcation Analysis in a Model of Hes1 Selfregulation with Time Delay</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Kejun%20Zhuang">Kejun Zhuang</a>, <a href="https://publications.waset.org/search?q=Hailong%20Zhu"> Hailong Zhu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The dynamics of a delayed mathematical model for Hes1 oscillatory expression are investigated. The linear stability of positive equilibrium and existence of local Hopf bifurcation are studied. Moreover, the global existence of large periodic solutions has been established due to the global bifurcation theorem. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Hes1" title="Hes1">Hes1</a>, <a href="https://publications.waset.org/search?q=Hopf%20bifurcation" title=" Hopf bifurcation"> Hopf bifurcation</a>, <a href="https://publications.waset.org/search?q=time%20delay" title=" time delay"> time delay</a>, <a href="https://publications.waset.org/search?q=transcriptional%20repression%20loop" title=" transcriptional repression loop"> transcriptional repression loop</a> </p> <a href="https://publications.waset.org/2496/stability-and-bifurcation-analysis-in-a-model-of-hes1-selfregulation-with-time-delay" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/2496/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/2496/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/2496/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/2496/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/2496/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/2496/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/2496/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/2496/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/2496/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/2496/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/2496.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1394</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">57</span> Periodic Orbits in a Delayed Nicholson's Blowflies Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Changjin%20Xu">Changjin Xu</a>, <a href="https://publications.waset.org/search?q=Peiluan%20Li"> Peiluan Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, a delayed Nicholson,s blowflies model with a linear harvesting term is investigated. Regarding the delay as a bifurcation parameter, we show that Hopf bifurcation will occur when the delay crosses a critical value. Numerical simulations supporting the theoretical findings are carried out.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Nicholson%27s%20blowflies%20model" title="Nicholson's blowflies model">Nicholson's blowflies model</a>, <a href="https://publications.waset.org/search?q=Stability" title=" Stability"> Stability</a>, <a href="https://publications.waset.org/search?q=Hopf%20bifurcation" title=" Hopf bifurcation"> Hopf bifurcation</a>, <a href="https://publications.waset.org/search?q=Delay." title=" Delay."> Delay.</a> </p> <a href="https://publications.waset.org/16966/periodic-orbits-in-a-delayed-nicholsons-blowflies-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16966/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16966/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16966/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16966/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16966/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16966/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16966/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16966/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16966/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16966/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16966.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1607</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">56</span> Stability and HOPF Bifurcation Analysis in a Stage-structured Predator-prey system with Two Time Delays</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Yongkun%20Li">Yongkun Li</a>, <a href="https://publications.waset.org/search?q=Meng%20Hu"> Meng Hu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>A stage-structured predator-prey system with two time delays is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated and the existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results. Based on the global Hopf bifurcation theorem for general functional differential equations, the global existence of periodic solutions is established.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Predator-prey%20system" title="Predator-prey system">Predator-prey system</a>, <a href="https://publications.waset.org/search?q=stage%20structure" title=" stage structure"> stage structure</a>, <a href="https://publications.waset.org/search?q=time%20delay" title=" time delay"> time delay</a>, <a href="https://publications.waset.org/search?q=HOPF%20bifurcation" title=" HOPF bifurcation"> HOPF bifurcation</a>, <a href="https://publications.waset.org/search?q=periodic%20solution" title=" periodic solution"> periodic solution</a>, <a href="https://publications.waset.org/search?q=stability." title=" stability."> stability.</a> </p> <a href="https://publications.waset.org/2083/stability-and-hopf-bifurcation-analysis-in-a-stage-structured-predator-prey-system-with-two-time-delays" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/2083/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/2083/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/2083/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/2083/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/2083/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/2083/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/2083/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/2083/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/2083/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/2083/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/2083.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1569</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">55</span> Bifurcation Analysis of a Delayed Predator-prey Fishery Model with Prey Reserve in Frequency Domain</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Changjin%20Xu">Changjin Xu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, applying frequency domain approach, a delayed predator-prey ﬁshery model with prey reserve is investigated. By choosing the delay τ as a bifurcation parameter, It is found that Hopf bifurcation occurs as the bifurcation parameter τ passes a sequence of critical values. That is, a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. The length of delay which preserves the stability of the positive equilibrium is calculated. Some numerical simulations are included to justify the theoretical analysis results. Finally, main conclusions are given.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Predator-prey%20model" title="Predator-prey model">Predator-prey model</a>, <a href="https://publications.waset.org/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/search?q=Hopf%20bifurcation" title=" Hopf bifurcation"> Hopf bifurcation</a>, <a href="https://publications.waset.org/search?q=frequency%20domain" title=" frequency domain"> frequency domain</a>, <a href="https://publications.waset.org/search?q=Nyquist%20criterion." title=" Nyquist criterion."> Nyquist criterion.</a> </p> <a href="https://publications.waset.org/13874/bifurcation-analysis-of-a-delayed-predator-prey-fishery-model-with-prey-reserve-in-frequency-domain" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/13874/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/13874/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/13874/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/13874/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/13874/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/13874/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/13874/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/13874/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/13874/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/13874/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/13874.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1404</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">54</span> Effect of Time Delay on the Transmission of Dengue Fever</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=K.%20Patanarapelert">K. Patanarapelert</a>, <a href="https://publications.waset.org/search?q=I.M.%20Tang"> I.M. Tang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The effect of a time delay on the transmission on dengue fever is studied. The time delay is due to the presence of an incubation period for the dengue virus to develop in the mosquito before the mosquito becomes infectious. The conditions for the existence of a Hopf bifurcation to limit cycle behavior are established. The conditions are different from the usual one and they are based on whether a particular third degree polynomial has positive real roots. A theorem for determining whether for a given set of parameter values, a critical delay time exist is given. It is found that for a set of realistic values of the parameters in the model, a Hopf bifurcation can not occur. For a set of unrealistic values of some of the parameters, it is shown that a Hopf bifurcation can occur. Numerical solutions using this last set show the trajectory of two of the variables making a transition from a spiraling orbit to a limit cycle orbit. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Dengue%20fever%20transmission" title="Dengue fever transmission">Dengue fever transmission</a>, <a href="https://publications.waset.org/search?q=time%20delay" title=" time delay"> time delay</a>, <a href="https://publications.waset.org/search?q=Hopfbifurcation" title=" Hopfbifurcation"> Hopfbifurcation</a>, <a href="https://publications.waset.org/search?q=limit%20cycle%20behavior" title=" limit cycle behavior"> limit cycle behavior</a> </p> <a href="https://publications.waset.org/12037/effect-of-time-delay-on-the-transmission-of-dengue-fever" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/12037/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/12037/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/12037/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/12037/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/12037/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/12037/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/12037/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/12037/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/12037/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/12037/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/12037.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1792</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">53</span> Bifurcations of a Delayed Prototype Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Changjin%20Xu">Changjin Xu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, a delayed prototype model is studied. Regarding the delay as a bifurcation parameter, we prove that a sequence of Hopf bifurcations will occur at the positive equilibrium when the delay increases. Using the normal form method and center manifold theory, some explicit formulae are worked out for determining the stability and the direction of the bifurcated periodic solutions. Finally, Computer simulations are carried out to explain some mathematical conclusions.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Prototype%20model" title="Prototype model">Prototype model</a>, <a href="https://publications.waset.org/search?q=Stability" title=" Stability"> Stability</a>, <a href="https://publications.waset.org/search?q=Hopf%20bifurcation" title=" Hopf bifurcation"> Hopf bifurcation</a>, <a href="https://publications.waset.org/search?q=Delay" title=" Delay"> Delay</a>, <a href="https://publications.waset.org/search?q=Periodic%20solution." title=" Periodic solution."> Periodic solution.</a> </p> <a href="https://publications.waset.org/1950/bifurcations-of-a-delayed-prototype-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1950/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1950/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/1950/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/1950/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/1950/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/1950/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/1950/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/1950/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/1950/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/1950/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/1950.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1662</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">52</span> Hopf Bifurcation Analysis for a Delayed Predator–prey System with Stage Structure</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Kejun%20Zhuang">Kejun Zhuang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a delayed predator–prey system with stage structure is investigated. Sufficient conditions for the system to have multiple periodic solutions are obtained when the delay is sufficiently large by applying Bendixson-s criterion. Further, some numerical examples are given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Predator-prey%20system" title="Predator-prey system">Predator-prey system</a>, <a href="https://publications.waset.org/search?q=Stage%20structure" title=" Stage structure"> Stage structure</a>, <a href="https://publications.waset.org/search?q=Hopf%20bifurcation" title=" Hopf bifurcation"> Hopf bifurcation</a>, <a href="https://publications.waset.org/search?q=Periodic%20solutions." title="Periodic solutions.">Periodic solutions.</a> </p> <a href="https://publications.waset.org/291/hopf-bifurcation-analysis-for-a-delayed-predator-prey-system-with-stage-structure" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/291/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/291/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/291/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/291/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/291/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/291/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/291/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/291/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/291/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/291/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/291.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1330</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">51</span> Global Existence of Periodic Solutions in a Delayed Tri–neuron Network</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Kejun%20Zhuang">Kejun Zhuang</a>, <a href="https://publications.waset.org/search?q=Zhaohui%20Wen"> Zhaohui Wen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a tri–neuron network model with time delay is investigated. By using the Bendixson-s criterion for high– dimensional ordinary differential equations and global Hopf bifurcation theory for functional differential equations, sufficient conditions for existence of periodic solutions when the time delay is sufficiently large are established. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Delay" title="Delay">Delay</a>, <a href="https://publications.waset.org/search?q=global%20Hopf%20bifurcation" title=" global Hopf bifurcation"> global Hopf bifurcation</a>, <a href="https://publications.waset.org/search?q=neural%20network" title=" neural network"> neural network</a>, <a href="https://publications.waset.org/search?q=periodicsolutions." title=" periodicsolutions."> periodicsolutions.</a> </p> <a href="https://publications.waset.org/1424/global-existence-of-periodic-solutions-in-a-delayed-tri-neuron-network" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1424/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1424/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/1424/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/1424/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/1424/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/1424/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/1424/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/1424/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/1424/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/1424/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/1424.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1483</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">50</span> Dynamics and Feedback Control for a New Hyperchaotic System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Kejun%20Zhuang">Kejun Zhuang</a>, <a href="https://publications.waset.org/search?q=Hailong%20Zhu"> Hailong Zhu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, stability and Hopf bifurcation analysis of a novel hyperchaotic system are investigated. Four feedback control strategies, the linear feedback control method, enhancing feedback control method, speed feedback control method and delayed feedback control method, are used to control the hyperchaotic attractor to unstable equilibrium. Moreover numerical simulations are given to verify the theoretical results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Feedback%20control" title="Feedback control">Feedback control</a>, <a href="https://publications.waset.org/search?q=Hopf%20bifurcation" title=" Hopf bifurcation"> Hopf bifurcation</a>, <a href="https://publications.waset.org/search?q=hyperchaotic%20system" title=" hyperchaotic system"> hyperchaotic system</a>, <a href="https://publications.waset.org/search?q=stability." title=" stability."> stability.</a> </p> <a href="https://publications.waset.org/1769/dynamics-and-feedback-control-for-a-new-hyperchaotic-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1769/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1769/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/1769/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/1769/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/1769/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/1769/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/1769/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/1769/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/1769/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/1769/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/1769.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1759</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">49</span> Bifurcations for a FitzHugh-Nagumo Model with Time Delays</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Changjin%20Xu">Changjin Xu</a>, <a href="https://publications.waset.org/search?q=Peiluan%20Li"> Peiluan Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, a FitzHugh-Nagumo model with time delays is investigated. The linear stability of the equilibrium and the existence of Hopf bifurcation with delay τ is investigated. By applying Nyquist criterion, the length of delay is estimated for which stability continues to hold. Numerical simulations for justifying the theoretical results are illustrated. Finally, main conclusions are given.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=FitzHugh-Nagumo%20model" title="FitzHugh-Nagumo model">FitzHugh-Nagumo model</a>, <a href="https://publications.waset.org/search?q=Time%20delay" title=" Time delay"> Time delay</a>, <a href="https://publications.waset.org/search?q=Stability" title=" Stability"> Stability</a>, <a href="https://publications.waset.org/search?q=Hopf%0D%0Abifurcation." title=" Hopf bifurcation."> Hopf bifurcation.</a> </p> <a href="https://publications.waset.org/16967/bifurcations-for-a-fitzhugh-nagumo-model-with-time-delays" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16967/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16967/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16967/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16967/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16967/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16967/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16967/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16967/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16967/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16967/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16967.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1690</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">48</span> Bifurcation Analysis of a Plankton Model with Discrete Delay</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Anuj%20Kumar%20Sharma">Anuj Kumar Sharma</a>, <a href="https://publications.waset.org/search?q=Amit%20Sharma"> Amit Sharma</a>, <a href="https://publications.waset.org/search?q=Kulbhushan%20Agnihotri"> Kulbhushan Agnihotri</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, a delayed plankton-nutrient interaction model consisting of phytoplankton, zooplankton and dissolved nutrient is considered. It is assumed that some species of phytoplankton releases toxin (known as toxin producing phytoplankton (TPP)) which is harmful for zooplankton growth and this toxin releasing process follows a discrete time variation. Using delay as bifurcation parameter, the stability of interior equilibrium point is investigated and it is shown that time delay can destabilize the otherwise stable non-zero equilibrium state by inducing Hopf-bifurcation when it crosses a certain threshold value. Explicit results are derived for stability and direction of the bifurcating periodic solution by using normal form theory and center manifold arguments. Finally, outcomes of the system are validated through numerical simulations.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Plankton" title="Plankton">Plankton</a>, <a href="https://publications.waset.org/search?q=Time%20delay" title=" Time delay"> Time delay</a>, <a href="https://publications.waset.org/search?q=Hopf-bifurcation" title=" Hopf-bifurcation"> Hopf-bifurcation</a>, <a href="https://publications.waset.org/search?q=Normal%20form%20theory" title=" Normal form theory"> Normal form theory</a>, <a href="https://publications.waset.org/search?q=Center%20manifold%20theorem." title=" Center manifold theorem."> Center manifold theorem.</a> </p> <a href="https://publications.waset.org/9997377/bifurcation-analysis-of-a-plankton-model-with-discrete-delay" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9997377/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9997377/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9997377/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9997377/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9997377/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9997377/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9997377/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9997377/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9997377/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9997377/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9997377.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1923</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">47</span> Analysis of a Spatiotemporal Phytoplankton Dynamics: Higher Order Stability and Pattern Formation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Randhir%20Singh%20Baghel">Randhir Singh Baghel</a>, <a href="https://publications.waset.org/search?q=Joydip%20Dhar"> Joydip Dhar</a>, <a href="https://publications.waset.org/search?q=Renu%20Jain"> Renu Jain</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, for the understanding of the phytoplankton dynamics in marine ecosystem, a susceptible and an infected class of phytoplankton population is considered in spatiotemporal domain. Here, the susceptible phytoplankton is growing logistically and the growth of infected phytoplankton is due to the instantaneous Holling type-II infection response function. The dynamics are studied in terms of the local and global stabilities for the system and further explore the possibility of Hopf -bifurcation, taking the half saturation period as (i.e., ) the bifurcation parameter in temporal domain. It is also observe that the reaction diffusion system exhibits spatiotemporal chaos and pattern formation in phytoplankton dynamics, which is particularly important role play for the spatially extended phytoplankton system. Also the effect of the diffusion coefficient on the spatial system for both one and two dimensional case is obtained. Furthermore, we explore the higher-order stability analysis of the spatial phytoplankton system for both linear and no-linear system. Finally, few numerical simulations are carried out for pattern formation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Phytoplankton%20dynamics" title="Phytoplankton dynamics">Phytoplankton dynamics</a>, <a href="https://publications.waset.org/search?q=Reaction-diffusion%20system" title=" Reaction-diffusion system"> Reaction-diffusion system</a>, <a href="https://publications.waset.org/search?q=Local%20stability" title=" Local stability"> Local stability</a>, <a href="https://publications.waset.org/search?q=Hopf-bifurcation" title=" Hopf-bifurcation"> Hopf-bifurcation</a>, <a href="https://publications.waset.org/search?q=Global%20stability" title=" Global stability"> Global stability</a>, <a href="https://publications.waset.org/search?q=Chaos" title=" Chaos"> Chaos</a>, <a href="https://publications.waset.org/search?q=Pattern%20Formation" title=" Pattern Formation"> Pattern Formation</a>, <a href="https://publications.waset.org/search?q=Higher-order%20stability%20analysis." title=" Higher-order stability analysis."> Higher-order stability analysis.</a> </p> <a href="https://publications.waset.org/12349/analysis-of-a-spatiotemporal-phytoplankton-dynamics-higher-order-stability-and-pattern-formation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/12349/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/12349/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/12349/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/12349/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/12349/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/12349/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/12349/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/12349/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/12349/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/12349/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/12349.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1650</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">46</span> Neuron Dynamics of Single-Compartment Traub Model for Hardware Implementations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=J.%20C.%20Moctezuma">J. C. Moctezuma</a>, <a href="https://publications.waset.org/search?q=V.%20Bre%C3%B1a-Medina"> V. Breña-Medina</a>, <a href="https://publications.waset.org/search?q=Jose%20Luis%20Nunez-Yanez"> Jose Luis Nunez-Yanez</a>, <a href="https://publications.waset.org/search?q=Joseph%20P.%20McGeehan">Joseph P. McGeehan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work we make a bifurcation analysis for a single compartment representation of Traub model, one of the most important conductance-based models. The analysis focus in two principal parameters: current and leakage conductance. Study of stable and unstable solutions are explored; also Hop-bifurcation and frequency interpretation when current varies is examined. This study allows having control of neuron dynamics and neuron response when these parameters change. Analysis like this is particularly important for several applications such as: tuning parameters in learning process, neuron excitability tests, measure bursting properties of the neuron, etc. Finally, a hardware implementation results were developed to corroborate these results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Traub%20model" title="Traub model">Traub model</a>, <a href="https://publications.waset.org/search?q=Pinsky-Rinzel%20model" title=" Pinsky-Rinzel model"> Pinsky-Rinzel model</a>, <a href="https://publications.waset.org/search?q=Hopf%0D%0Abifurcation" title=" Hopf bifurcation"> Hopf bifurcation</a>, <a href="https://publications.waset.org/search?q=single-compartment%20models" title=" single-compartment models"> single-compartment models</a>, <a href="https://publications.waset.org/search?q=Bifurcation%20analysis" title=" Bifurcation analysis"> Bifurcation analysis</a>, <a href="https://publications.waset.org/search?q=neuron%0D%0Amodeling." title=" neuron modeling."> neuron modeling.</a> </p> <a href="https://publications.waset.org/10003625/neuron-dynamics-of-single-compartment-traub-model-for-hardware-implementations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10003625/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10003625/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10003625/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10003625/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10003625/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10003625/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10003625/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10003625/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10003625/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10003625/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10003625.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1205</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">45</span> Chatter Stability Characterization of Full-Immersion End-Milling Using a Generalized Modified Map of the Full-Discretization Method, Part 1: Validation of Results and Study of Stability Lobes by Numerical Simulation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Chigbogu%20G.%20Ozoegwu">Chigbogu G. Ozoegwu</a>, <a href="https://publications.waset.org/search?q=Sam%20N.%20Omenyi"> Sam N. Omenyi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The objective in this work is to generate and discuss the stability results of fully-immersed end-milling process with parameters; tool mass m=0.0431kg,tool natural frequency ω<sub>n</sub> = 5700 rads^-1, damping factor ξ=0.002 and workpiece cutting coefficient C=3.5x10^7 Nm^-7/4. Different no of teeth is considered for the end-milling. Both 1-DOF and 2-DOF chatter models of the system are generated on the basis of non-linear force law. Chatter stability analysis is carried out using a modified form (generalized for both 1-DOF and 2-DOF models) of recently developed method called Full-discretization. The full-immersion three tooth end-milling together with higher toothed end-milling processes has secondary Hopf bifurcation lobes (SHBL’s) that exhibit one turning (minimum) point each. Each of such SHBL is demarcated by its minimum point into two portions; (i) the Lower Spindle Speed Portion (LSSP) in which bifurcations occur in the right half portion of the unit circle centred at the origin of the complex plane and (ii) the Higher Spindle Speed Portion (HSSP) in which bifurcations occur in the left half portion of the unit circle. Comments are made regarding why bifurcation lobes should generally get bigger and more visible with increase in spindle speed and why flip bifurcation lobes (FBL’s) could be invisible in the low-speed stability chart but visible in the high-speed stability chart of the fully-immersed three-tooth miller.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Chatter" title="Chatter">Chatter</a>, <a href="https://publications.waset.org/search?q=flip%20bifurcation" title=" flip bifurcation"> flip bifurcation</a>, <a href="https://publications.waset.org/search?q=modified%20full-discretization%20map%20stability%20lobe" title=" modified full-discretization map stability lobe"> modified full-discretization map stability lobe</a>, <a href="https://publications.waset.org/search?q=secondary%20Hopf%20bifurcation." title=" secondary Hopf bifurcation. "> secondary Hopf bifurcation. </a> </p> <a href="https://publications.waset.org/9996994/chatter-stability-characterization-of-full-immersion-end-milling-using-a-generalized-modified-map-of-the-full-discretization-method-part-1-validation-of-results-and-study-of-stability-lobes-by-numerical-simulation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9996994/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9996994/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9996994/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9996994/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9996994/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9996994/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9996994/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9996994/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9996994/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9996994/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9996994.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1832</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">44</span> Bifurcations and Chaotic Solutions of Two-dimensional Zonal Jet Flow on a Rotating Sphere</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Eiichi%20Sasaki">Eiichi Sasaki</a>, <a href="https://publications.waset.org/search?q=Shin-ichi%20Takehiro"> Shin-ichi Takehiro</a>, <a href="https://publications.waset.org/search?q=Michio%20Yamada"> Michio Yamada</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We study bifurcation structure of the zonal jet flow the streamfunction of which is expressed by a single spherical harmonics on a rotating sphere. In the non-rotating case, we find that a steady traveling wave solution arises from the zonal jet flow through Hopf bifurcation. As the Reynolds number increases, several traveling solutions arise only through the pitchfork bifurcations and at high Reynolds number the bifurcating solutions become Hopf unstable. In the rotating case, on the other hand, under the stabilizing effect of rotation, as the absolute value of rotation rate increases, the number of the bifurcating solutions arising from the zonal jet flow decreases monotonically. We also carry out time integration to study unsteady solutions at high Reynolds number and find that in the non-rotating case the unsteady solutions are chaotic, while not in the rotating cases calculated. This result reflects the general tendency that the rotation stabilizes nonlinear solutions of Navier-Stokes equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=rotating%20sphere" title="rotating sphere">rotating sphere</a>, <a href="https://publications.waset.org/search?q=two-dimensional%20flow" title=" two-dimensional flow"> two-dimensional flow</a>, <a href="https://publications.waset.org/search?q=bifurcationstructure" title=" bifurcationstructure"> bifurcationstructure</a> </p> <a href="https://publications.waset.org/10566/bifurcations-and-chaotic-solutions-of-two-dimensional-zonal-jet-flow-on-a-rotating-sphere" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10566/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10566/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10566/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10566/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10566/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10566/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10566/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10566/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10566/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10566/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10566.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1650</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">43</span> Mathematical Model of Depletion of Forestry Resource: Effect of Synthetic Based Industries</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Manisha%20Chaudhary">Manisha Chaudhary</a>, <a href="https://publications.waset.org/search?q=Joydip%20Dhar"> Joydip Dhar</a>, <a href="https://publications.waset.org/search?q=Govind%20Prasad%20Sahu"> Govind Prasad Sahu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>A mathematical model is proposed considering the forest biomass density B(t), density of wood based industries W(t) and density of synthetic industries S(t). It is assumed that the forest biomass grows logistically in the absence of wood based industries, but depletion of forestry biomass is due to presence of wood based industries. The growth of wood based industries depends on B(t), while S(t) grows at a constant rate, independent of B(t). Further there is a competition between W(t) and S(t) according to market demand. The proposed model has four ecologically feasible steady states, namely, E1: forest biomass free and wood industries free equilibrium; E2: wood industries free equilibrium and two coexisting equilibria E&lowast;1 , E&lowast;2 . Behavior of the system near all feasible equilibria is analyzed using the stability theory of differential equations. In the proposed model, the natural depletion rate h1 is a crucial parameter and system exhibits Hopf-bifurcation about the non-trivial equilibrium with respect to h1. The analytical results are verified using numerical simulation.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=A%20mathematical%20model" title="A mathematical model">A mathematical model</a>, <a href="https://publications.waset.org/search?q=Competition%20between%20wood%20based%20and%20synthetic%20industries" title=" Competition between wood based and synthetic industries"> Competition between wood based and synthetic industries</a>, <a href="https://publications.waset.org/search?q=Hopf-bifurcation" title=" Hopf-bifurcation"> Hopf-bifurcation</a>, <a href="https://publications.waset.org/search?q=Stability%20analysis." title=" Stability analysis."> Stability analysis.</a> </p> <a href="https://publications.waset.org/16903/mathematical-model-of-depletion-of-forestry-resource-effect-of-synthetic-based-industries" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16903/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16903/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16903/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16903/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16903/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16903/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16903/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16903/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16903/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16903/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16903.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">3498</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">42</span> Bifurcation Study and Parameter Analyses Boost Converter</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=S.%20Ben%20Said">S. Ben Said</a>, <a href="https://publications.waset.org/search?q=K.%20Ben%20Saad"> K. Ben Saad</a>, <a href="https://publications.waset.org/search?q=M.%20Benrejeb"> M. Benrejeb</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This paper deals with bifurcation analyses in current programmed DC/DC Boost converter and exhibition of chaotic behavior. This phenomenon occurs due to variation of a set of the studied circuit parameters (input voltage and a reference current). Two different types of bifurcation paths have been observed as part as part of another bifurcation arising from variation of suitable chosen parameter.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Bifurcation" title="Bifurcation">Bifurcation</a>, <a href="https://publications.waset.org/search?q=Chaos" title=" Chaos"> Chaos</a>, <a href="https://publications.waset.org/search?q=Boost%20converter" title=" Boost converter"> Boost converter</a>, <a href="https://publications.waset.org/search?q=Current-%20programmed%20control" title=" Current- programmed control"> Current- programmed control</a>, <a href="https://publications.waset.org/search?q=Initial%20parameters." title=" Initial parameters. "> Initial parameters. </a> </p> <a href="https://publications.waset.org/9997716/bifurcation-study-and-parameter-analyses-boost-converter" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9997716/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9997716/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9997716/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9997716/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9997716/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9997716/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9997716/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9997716/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9997716/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9997716/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9997716.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2417</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">41</span> Fixed Point Equations Related to Motion Integrals in Renormalization Hopf Algebra</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ali%20Shojaei-Fard">Ali Shojaei-Fard</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we consider quantum motion integrals depended on the algebraic reconstruction of BPHZ method for perturbative renormalization in two different procedures. Then based on Bogoliubov character and Baker-Campbell-Hausdorff (BCH) formula, we show that how motion integral condition on components of Birkhoff factorization of a Feynman rules character on Connes- Kreimer Hopf algebra of rooted trees can determine a family of fixed point equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Birkhoff%20Factorization" title="Birkhoff Factorization">Birkhoff Factorization</a>, <a href="https://publications.waset.org/search?q=Connes-Kreimer%20Hopf%20Algebra%20of%20Rooted%20Trees" title=" Connes-Kreimer Hopf Algebra of Rooted Trees"> Connes-Kreimer Hopf Algebra of Rooted Trees</a>, <a href="https://publications.waset.org/search?q=Integral%20Renormalization" title=" Integral Renormalization"> Integral Renormalization</a>, <a href="https://publications.waset.org/search?q=Lax%20Pair%20Equation" title=" Lax Pair Equation"> Lax Pair Equation</a>, <a href="https://publications.waset.org/search?q=Rota-%20Baxter%20Algebras." title=" Rota- Baxter Algebras."> Rota- Baxter Algebras.</a> </p> <a href="https://publications.waset.org/6710/fixed-point-equations-related-to-motion-integrals-in-renormalization-hopf-algebra" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/6710/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/6710/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/6710/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/6710/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/6710/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/6710/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/6710/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/6710/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/6710/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/6710/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/6710.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1443</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">40</span> Transmission Model for Plasmodium Vivax Malaria: Conditions for Bifurcation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=P.%20Pongsumpun">P. Pongsumpun</a>, <a href="https://publications.waset.org/search?q=I.M.%20Tang"> I.M. Tang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Plasmodium vivax malaria differs from P. falciparum malaria in that a person suffering from P. vivax infection can suffer relapses of the disease. This is due the parasite being able to remain dormant in the liver of the patients where it is able to re-infect the patient after a passage of time. During this stage, the patient is classified as being in the dormant class. The model to describe the transmission of P. vivax malaria consists of a human population divided into four classes, the susceptible, the infected, the dormant and the recovered. The effect of a time delay on the transmission of this disease is studied. The time delay is the period in which the P. vivax parasite develops inside the mosquito (vector) before the vector becomes infectious (i.e., pass on the infection). We analyze our model by using standard dynamic modeling method. Two stable equilibrium states, a disease free state E0 and an endemic state E1, are found to be possible. It is found that the E0 state is stable when a newly defined basic reproduction number G is less than one. If G is greater than one the endemic state E1 is stable. The conditions for the endemic equilibrium state E1 to be a stable spiral node are established. For realistic values of the parameters in the model, it is found that solutions in phase space are trajectories spiraling into the endemic state. It is shown that the limit cycle and chaotic behaviors can only be achieved with unrealistic parameter values.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Equilibrium%20states" title="Equilibrium states">Equilibrium states</a>, <a href="https://publications.waset.org/search?q=Hopf%20bifurcation" title=" Hopf bifurcation"> Hopf bifurcation</a>, <a href="https://publications.waset.org/search?q=limit%20cyclebehavior" title=" limit cyclebehavior"> limit cyclebehavior</a>, <a href="https://publications.waset.org/search?q=local%20stability" title=" local stability"> local stability</a>, <a href="https://publications.waset.org/search?q=Plasmodium%20Vivax" title=" Plasmodium Vivax"> Plasmodium Vivax</a>, <a href="https://publications.waset.org/search?q=time%20delay." title=" time delay."> time delay.</a> </p> <a href="https://publications.waset.org/102/transmission-model-for-plasmodium-vivax-malaria-conditions-for-bifurcation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/102/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/102/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/102/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/102/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/102/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/102/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/102/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/102/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/102/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/102/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/102.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2243</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">39</span> Nonlinear Dynamics of Cracked RC Beams under Harmonic Excitation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Atul%20Krishna%20Banik">Atul Krishna Banik</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Nonlinear response behaviour of a cracked RC beam under harmonic excitation is analysed to investigate various instability phenomena like, bifurcation, jump phenomena etc. The nonlinearity of the system arises due to opening and closing of the cracks in the RC beam and is modelled as a cubic polynomial. In order to trace different branches at the bifurcation point on the response curve (amplitude versus frequency of excitation plot), an arc length continuation technique along with the incremental harmonic balance (IHBC) method is employed. The stability of the solution is investigated by the Floquet theory using Hsu-s scheme. The periodic solutions obtained by the IHBC method are compared with these obtained by the numerical integration of the equation of motion. Characteristics of solutions fold bifurcation, jump phenomena and from stable to unstable zones are identified.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Incremental%20harmonic%20balance" title="Incremental harmonic balance">Incremental harmonic balance</a>, <a href="https://publications.waset.org/search?q=arc-length%20continuation" title=" arc-length continuation"> arc-length continuation</a>, <a href="https://publications.waset.org/search?q=bifurcation" title=" bifurcation"> bifurcation</a>, <a href="https://publications.waset.org/search?q=jump%20phenomena." title=" jump phenomena."> jump phenomena.</a> </p> <a href="https://publications.waset.org/13749/nonlinear-dynamics-of-cracked-rc-beams-under-harmonic-excitation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/13749/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/13749/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/13749/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/13749/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/13749/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/13749/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/13749/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/13749/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/13749/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/13749/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/13749.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1522</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">38</span> Stability and Bifurcation Analysis of a Discrete Gompertz Model with Time Delay</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Yingguo%20Li">Yingguo Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, we consider a discrete Gompertz model with time delay. Firstly, the stability of the equilibrium of the system is investigated by analyzing the characteristic equation. By choosing the time delay as a bifurcation parameter, we prove that Neimark- Sacker bifurcations occur when the delay passes a sequence of critical values. The direction and stability of the Neimark-Sacker are determined by using normal forms and centre manifold theory. Finally, some numerical simulations are given to verify the theoretical analysis.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Gompertz%20system" title="Gompertz system">Gompertz system</a>, <a href="https://publications.waset.org/search?q=Neimark-Sacker%20bifurcation" title=" Neimark-Sacker bifurcation"> Neimark-Sacker bifurcation</a>, <a href="https://publications.waset.org/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/search?q=time%20delay." title=" time delay."> time delay.</a> </p> <a href="https://publications.waset.org/15238/stability-and-bifurcation-analysis-of-a-discrete-gompertz-model-with-time-delay" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/15238/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/15238/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/15238/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/15238/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/15238/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/15238/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/15238/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/15238/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/15238/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/15238/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/15238.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1941</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">37</span> CFD Analysis of the Blood Flow in Left Coronary Bifurcation with Variable Angulation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Midiya%20Khademi">Midiya Khademi</a>, <a href="https://publications.waset.org/search?q=Ali%20Nikoo"> Ali Nikoo</a>, <a href="https://publications.waset.org/search?q=Shabnam%20Rahimnezhad%20Baghche%20Jooghi"> Shabnam Rahimnezhad Baghche Jooghi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Cardiovascular diseases (CVDs) are the main cause of death globally. Most CVDs can be prevented by avoiding habitual risk factors. Separate from the habitual risk factors, there are some inherent factors in each individual that can increase the risk potential of CVDs. Vessel shapes and geometry are influential factors, having great impact on the blood flow and the hemodynamic behavior of the vessels. In the present study, the influence of bifurcation angle on blood flow characteristics is studied. In order to approach this topic, by simplifying the details of the bifurcation, three models with angles 30°, 45°, and 60° were created, then by using CFD analysis, the response of these models for stable flow and pulsatile flow was studied. In the conducted simulation in order to eliminate the influence of other geometrical factors, only the angle of the bifurcation was changed and other parameters remained constant during the research. Simulations are conducted under dynamic and stable condition. In the stable flow simulation, a steady velocity of 0.17 m/s at the inlet plug was maintained and in dynamic simulations, a typical LAD flow waveform is implemented. The results show that the bifurcation angle has an influence on the maximum speed of the flow. In the stable flow condition, increasing the angle lead to decrease the maximum flow velocity. In the dynamic flow simulations, increasing the bifurcation angle lead to an increase in the maximum velocity. Since blood flow has pulsatile characteristics, using a uniform velocity during the simulations can lead to a discrepancy between the actual results and the calculated results.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Coronary%20artery" title="Coronary artery">Coronary artery</a>, <a href="https://publications.waset.org/search?q=cardiovascular%20disease" title=" cardiovascular disease"> cardiovascular disease</a>, <a href="https://publications.waset.org/search?q=bifurcation" title=" bifurcation"> bifurcation</a>, <a href="https://publications.waset.org/search?q=atherosclerosis" title=" atherosclerosis"> atherosclerosis</a>, <a href="https://publications.waset.org/search?q=CFD" title=" CFD"> CFD</a>, <a href="https://publications.waset.org/search?q=artery%20wall%20shear%20stress." title=" artery wall shear stress."> artery wall shear stress.</a> </p> <a href="https://publications.waset.org/10010110/cfd-analysis-of-the-blood-flow-in-left-coronary-bifurcation-with-variable-angulation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10010110/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10010110/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10010110/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10010110/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10010110/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10010110/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10010110/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10010110/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10010110/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10010110/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10010110.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">953</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">36</span> Bifurcation Method for Solving Positive Solutions to a Class of Semilinear Elliptic Equations and Stability Analysis of Solutions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Hailong%20Zhu">Hailong Zhu</a>, <a href="https://publications.waset.org/search?q=Zhaoxiang%20Li"> Zhaoxiang Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Semilinear elliptic equations are ubiquitous in natural sciences. They give rise to a variety of important phenomena in quantum mechanics, nonlinear optics, astrophysics, etc because they have rich multiple solutions. But the nontrivial solutions of semilinear equations are hard to be solved for the lack of stabilities, such as Lane-Emden equation, Henon equation and Chandrasekhar equation. In this paper, bifurcation method is applied to solving semilinear elliptic equations which are with homogeneous Dirichlet boundary conditions in 2D. Using this method, nontrivial numerical solutions will be computed and visualized in many different domains (such as square, disk, annulus, dumbbell, etc).</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Semilinear%20elliptic%20equations" title="Semilinear elliptic equations">Semilinear elliptic equations</a>, <a href="https://publications.waset.org/search?q=positive%20solutions" title=" positive solutions"> positive solutions</a>, <a href="https://publications.waset.org/search?q=bifurcation%20method" title=" bifurcation method"> bifurcation method</a>, <a href="https://publications.waset.org/search?q=isotropy%20subgroups." title=" isotropy subgroups."> isotropy subgroups.</a> </p> <a href="https://publications.waset.org/9287/bifurcation-method-for-solving-positive-solutions-to-a-class-of-semilinear-elliptic-equations-and-stability-analysis-of-solutions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9287/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9287/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9287/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9287/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9287/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9287/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9287/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9287/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9287/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9287/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9287.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1648</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">35</span> Haemodynamics Study in Subject Specific Carotid Bifurcation Using FSI</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=S.%20M.%20Abdul%20Khader">S. M. Abdul Khader</a>, <a href="https://publications.waset.org/search?q=Anurag%20Ayachit"> Anurag Ayachit</a>, <a href="https://publications.waset.org/search?q=Raghuvir%20Pai"> Raghuvir Pai</a>, <a href="https://publications.waset.org/search?q=K.%20A.%20Ahmed"> K. A. Ahmed</a>, <a href="https://publications.waset.org/search?q=V.%20R.%20K.%20Rao"> V. R. K. Rao</a>, <a href="https://publications.waset.org/search?q=S.%20Ganesh%20Kamath"> S. Ganesh Kamath</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The numerical simulation has made tremendous advances in investigating the blood flow phenomenon through elastic arteries. Such study can be useful in demonstrating the disease progression and hemodynamics of cardiovascular diseases such as atherosclerosis. In the present study, patient specific case diagnosed with partially stenosed complete right ICA and normal left carotid bifurcation without any atherosclerotic plaque formation is considered. 3D patient specific carotid bifurcation model is generated based on CT scan data using MIMICS-4.0 and numerical analysis is performed using FSI solver in ANSYS-14.5. The blood flow is assumed to be incompressible, homogenous and Newtonian, while the artery wall is assumed to be linearly elastic. The two-way sequentially coupled transient FSI analysis is performed using FSI solver for three pulse cycles. The hemodynamic parameters such as flow pattern, Wall Shear Stress, pressure contours and arterial wall deformation are studied at the bifurcation and critical zones such as stenosis. The variation in flow behavior is studied throughout the pulse cycle. Also, the simulation results reveal that there is a considerable increase in the flow behavior in stenosed carotid in contrast to the normal carotid bifurcation system. The investigation also demonstrates the disturbed flow pattern especially at the bifurcation and stenosed zone elevating the hemodynamics, particularly during peak systole and later part of the pulse cycle. The results obtained agree well with the clinical observation and demonstrates the potential of patient specific numerical studies in prognosis of disease progression and plaque rupture. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fluid-Structure%20Interaction" title="Fluid-Structure Interaction">Fluid-Structure Interaction</a>, <a href="https://publications.waset.org/search?q=arterial%20stenosis" title=" arterial stenosis"> arterial stenosis</a>, <a href="https://publications.waset.org/search?q=Wall%0D%0AShear%20Stress" title=" Wall Shear Stress"> Wall Shear Stress</a>, <a href="https://publications.waset.org/search?q=Carotid%20Artery%20Bifurcation." title=" Carotid Artery Bifurcation."> Carotid Artery Bifurcation.</a> </p> <a href="https://publications.waset.org/10001815/haemodynamics-study-in-subject-specific-carotid-bifurcation-using-fsi" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10001815/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10001815/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10001815/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10001815/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10001815/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10001815/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10001815/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10001815/ris" target="_blank" rel="nofollow" class="btn 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