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Search results for: Changjin Xu

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class="col-md-9 mx-auto"> <form method="get" action="https://publications.waset.org/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="Changjin Xu"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 12</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: Changjin Xu</h1> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">12</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">11</span> Periodic Orbits in a Delayed Nicholson&#039;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&nbsp;with a linear harvesting term is investigated. Regarding the delay as a&nbsp;bifurcation parameter, we show that Hopf bifurcation will occur when&nbsp;the delay crosses a critical value. Numerical simulations supporting&nbsp;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&#039;s blowflies model">Nicholson&#039;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">10</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">9</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">8</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&nbsp;delays is investigated. The linear stability of the equilibrium and&nbsp;the existence of Hopf bifurcation with delay &tau; is investigated. By&nbsp;applying Nyquist criterion, the length of delay is estimated for which&nbsp;stability continues to hold. Numerical simulations for justifying the&nbsp;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">7</span> Periodic Solutions for a Two-prey One-predator System on Time Scales</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, using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales, the existence of periodic solutions for a two-prey one-predator system is studied. Some sufficient conditions for the existence of positive periodic solutions are obtained. The results provide unified existence theorems of periodic solution for the continuous differential equations and discrete difference equations.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Time%20scales" title="Time scales">Time scales</a>, <a href="https://publications.waset.org/search?q=competitive%20system" title=" competitive system"> competitive system</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=coincidence%20degree" title=" coincidence degree"> coincidence degree</a>, <a href="https://publications.waset.org/search?q=topological%20degree." title=" topological degree."> topological degree.</a> </p> <a href="https://publications.waset.org/5256/periodic-solutions-for-a-two-prey-one-predator-system-on-time-scales" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/5256/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/5256/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/5256/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/5256/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/5256/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/5256/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/5256/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/5256/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/5256/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/5256/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/5256.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">1369</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">6</span> Positive Periodic Solutions in a Discrete Competitive System with the Effect of Toxic Substances</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=Qianhong%20Zhang"> Qianhong Zhang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, a delayed competitive system with the effect of toxic substances is investigated. With the aid of differential equations with piecewise constant arguments, a discrete analogue of continuous non-autonomous delayed competitive system with the effect of toxic substances is proposed. By using Gaines and Mawhin,s continuation theorem of coincidence degree theory, a easily verifiable sufficient condition for the existence of positive solutions of difference equations is obtained.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Competitive%20system" title="Competitive system">Competitive system</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=discrete%20time%20delay" title=" discrete time delay"> discrete time delay</a>, <a href="https://publications.waset.org/search?q=topological%20degree." title=" topological degree."> topological degree.</a> </p> <a href="https://publications.waset.org/15619/positive-periodic-solutions-in-a-discrete-competitive-system-with-the-effect-of-toxic-substances" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/15619/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/15619/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/15619/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/15619/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/15619/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/15619/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/15619/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/15619/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/15619/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/15619/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/15619.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">1456</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">5</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 &alpha; as a bifurcation parameter, it is found that Hopf bifurcation occurs as the bifurcation parameter &alpha; 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">4</span> Uniformly Strong Persistence for a Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes</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> <p>In this paper, a asymptotically periodic predator-prey model with Modified Leslie-Gower and Holling-Type II schemes is investigated. Some sufficient conditions for the uniformly strong persistence of the system are established. Our result is an important complementarity to the earlier results.</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=uniformly%20strong%20persistence" title=" uniformly strong persistence"> uniformly strong persistence</a>, <a href="https://publications.waset.org/search?q=asymptotically%20periodic" title=" asymptotically periodic"> asymptotically periodic</a>, <a href="https://publications.waset.org/search?q=Holling-type%20II." title=" Holling-type II."> Holling-type II.</a> </p> <a href="https://publications.waset.org/10002694/uniformly-strong-persistence-for-a-predator-prey-model-with-modified-leslie-gower-and-holling-type-ii-schemes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10002694/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10002694/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10002694/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10002694/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10002694/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10002694/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10002694/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10002694/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10002694/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10002694/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10002694.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">2055</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">3</span> Stability Analysis in a Fractional Order Delayed Predator-Prey 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, we study the stability of a fractional order&nbsp;delayed predator-prey model. By using the Laplace transform, we&nbsp;introduce a characteristic equation for the above system. It is shown&nbsp;that if all roots of the characteristic equation have negative parts, then&nbsp;the equilibrium of the above fractional order predator-prey system is&nbsp;Lyapunov globally asymptotical stable. An example is given to show&nbsp;the effectiveness of the approach presented in this paper.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20predator-prey%20model" title="Fractional predator-prey model">Fractional predator-prey model</a>, <a href="https://publications.waset.org/search?q=laplace%20transform" title=" laplace transform"> laplace transform</a>, <a href="https://publications.waset.org/search?q=characteristic%20equation." title=" characteristic equation."> characteristic equation.</a> </p> <a href="https://publications.waset.org/16751/stability-analysis-in-a-fractional-order-delayed-predator-prey-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16751/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16751/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16751/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16751/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16751/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16751/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16751/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16751/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16751/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16751/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16751.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">2497</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">2</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 铿乻hery model with prey reserve is investigated. By choosing the delay &tau; as a bifurcation parameter, It is found that Hopf bifurcation occurs as the bifurcation parameter &tau; 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">1</span> Periodic Solutions in a Delayed Competitive System with the Effect of Toxic Substances on Time Scales</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=Qianhong%20Zhang"> Qianhong Zhang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, the existence of periodic solutions of a delayed competitive system with the effect of toxic substances is investigated by using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales. New sufficient conditions are obtained for the existence of periodic solutions. The approach is unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations. Moreover, The approach has been widely applied to study existence of periodic solutions in differential equations and difference equations.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Time%20scales" title="Time scales">Time scales</a>, <a href="https://publications.waset.org/search?q=competitive%20system" title=" competitive system"> competitive system</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=coincidence%20degree" title=" coincidence degree"> coincidence degree</a>, <a href="https://publications.waset.org/search?q=topological%20degree." title=" topological degree."> topological degree.</a> </p> <a href="https://publications.waset.org/15291/periodic-solutions-in-a-delayed-competitive-system-with-the-effect-of-toxic-substances-on-time-scales" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/15291/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/15291/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/15291/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/15291/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/15291/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/15291/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/15291/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/15291/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a 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