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drive-response dynamical network</title> <meta name="description" content="Search results for: drive-response dynamical network"> <meta name="keywords" content="drive-response dynamical network"> <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 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method="get" action="https://publications.waset.org/abstracts/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="drive-response dynamical network"> <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> 4959</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: drive-response dynamical network</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4959</span> Dynamical Systems and Fibonacci Numbers</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Vandana%20N.%20Purav">Vandana N. Purav</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Dynamical systems concept is a mathematical formalization for any fixed rule that describes the time dependence of a points position in its ambient space. e.g. pendulum of a clock, the number of fish each spring in a lake, the number of rabbits spring in an enclosure, etc. The Dynamical system theory used to describe the complex nature that is dynamical systems with differential equations called continuous dynamical system or dynamical system with difference equations called discrete dynamical system. The concept of dynamical system has its origin in Newtonian mechanics. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dynamical%20systems" title="dynamical systems">dynamical systems</a>, <a href="https://publications.waset.org/abstracts/search?q=Fibonacci%20numbers" title=" Fibonacci numbers"> Fibonacci numbers</a>, <a href="https://publications.waset.org/abstracts/search?q=Newtonian%20mechanics" title=" Newtonian mechanics"> Newtonian mechanics</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete%20dynamical%20system" title=" discrete dynamical system"> discrete dynamical system</a> </p> <a href="https://publications.waset.org/abstracts/25870/dynamical-systems-and-fibonacci-numbers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/25870.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">492</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4958</span> Projective Lag Synchronization in Drive-Response Dynamical Networks via Hybrid Feedback Control</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohd%20Salmi%20Md%20Noorani">Mohd Salmi Md Noorani</a>, <a href="https://publications.waset.org/abstracts/search?q=Ghada%20Al-Mahbashi"> Ghada Al-Mahbashi</a>, <a href="https://publications.waset.org/abstracts/search?q=Sakhinah%20Abu%20Bakar"> Sakhinah Abu Bakar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper investigates projective lag synchronization (PLS) behavior in drive response dynamical networks (DRDNs) model with identical nodes. A hybrid feedback control method is designed to achieve the PLS with mismatch and without mismatch terms. The stability of the error dynamics is proven theoretically using the Lyapunov stability theory. Finally, analytical results show that the states of the dynamical network with non-delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Moreover, the numerical simulations results demonstrate the validity of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=drive-response%20dynamical%20network" title="drive-response dynamical network">drive-response dynamical network</a>, <a href="https://publications.waset.org/abstracts/search?q=projective%20lag%20synchronization" title=" projective lag synchronization"> projective lag synchronization</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20feedback%20control" title=" hybrid feedback control"> hybrid feedback control</a>, <a href="https://publications.waset.org/abstracts/search?q=stability%20theory" title=" stability theory"> stability theory</a> </p> <a href="https://publications.waset.org/abstracts/14139/projective-lag-synchronization-in-drive-response-dynamical-networks-via-hybrid-feedback-control" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/14139.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">391</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4957</span> Neural Adaptive Controller for a Class of Nonlinear Pendulum Dynamical System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Reza%20Rahimi%20Khoygani">Mohammad Reza Rahimi Khoygani</a>, <a href="https://publications.waset.org/abstracts/search?q=Reza%20Ghasemi"> Reza Ghasemi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, designing direct adaptive neural controller is applied for a class of a nonlinear pendulum dynamic system. The radial basis function (RBF) is used for the Neural network (NN). The adaptive neural controller is robust in presence of external and internal uncertainties. Both the effectiveness of the controller and robustness against disturbances are the merits of this paper. The promising performance of the proposed controllers investigates in simulation results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adaptive%20control" title="adaptive control">adaptive control</a>, <a href="https://publications.waset.org/abstracts/search?q=pendulum%20dynamical%20system" title=" pendulum dynamical system"> pendulum dynamical system</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20control" title=" nonlinear control"> nonlinear control</a>, <a href="https://publications.waset.org/abstracts/search?q=adaptive%20neural%20controller" title=" adaptive neural controller"> adaptive neural controller</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20dynamical" title=" nonlinear dynamical"> nonlinear dynamical</a>, <a href="https://publications.waset.org/abstracts/search?q=neural%20network" title=" neural network"> neural network</a>, <a href="https://publications.waset.org/abstracts/search?q=RBF" title=" RBF"> RBF</a>, <a href="https://publications.waset.org/abstracts/search?q=driven%20pendulum" title=" driven pendulum"> driven pendulum</a>, <a href="https://publications.waset.org/abstracts/search?q=position%20control" title=" position control "> position control </a> </p> <a href="https://publications.waset.org/abstracts/13649/neural-adaptive-controller-for-a-class-of-nonlinear-pendulum-dynamical-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/13649.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">670</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4956</span> An Inverse Optimal Control Approach for the Nonlinear System Design Using ANN</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20P.%20Nanda%20Kumar">M. P. Nanda Kumar</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20Dheeraj"> K. Dheeraj</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The design of a feedback controller, so as to minimize a given performance criterion, for a general non-linear dynamical system is difficult; if not impossible. But for a large class of non-linear dynamical systems, the open loop control that minimizes a performance criterion can be obtained using calculus of variations and Pontryagin’s minimum principle. In this paper, the open loop optimal trajectories, that minimizes a given performance measure, is used to train the neural network whose inputs are state variables of non-linear dynamical systems and the open loop optimal control as the desired output. This trained neural network is used as the feedback controller. In other words, attempts are made here to solve the “inverse optimal control problem” by using the state and control trajectories that are optimal in an open loop sense. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=inverse%20optimal%20control" title="inverse optimal control">inverse optimal control</a>, <a href="https://publications.waset.org/abstracts/search?q=radial%20basis%20function" title=" radial basis function"> radial basis function</a>, <a href="https://publications.waset.org/abstracts/search?q=neural%20network" title=" neural network"> neural network</a>, <a href="https://publications.waset.org/abstracts/search?q=controller%20design" title=" controller design"> controller design</a> </p> <a href="https://publications.waset.org/abstracts/9888/an-inverse-optimal-control-approach-for-the-nonlinear-system-design-using-ann" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/9888.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">553</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4955</span> Modeling and Controlling Nonlinear Dynamical Effects in Non-Contact Superconducting and Diamagnetic Suspensions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sergey%20Kuznetsov">Sergey Kuznetsov</a>, <a href="https://publications.waset.org/abstracts/search?q=Yuri%20Urman"> Yuri Urman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We present an approach to investigate non-linear dynamical effects occurring in the noncontact superconducting and diamagnetic suspensions, when levitated body has finite size. This approach is based on the calculation of interaction energy between spherical finite size superconducting or diamagnetic body with external magnetic field. Effects of small deviations from spherical shape may be also taken into account by introducing small corrections to the energy. This model allows investigating dynamical effects important for practical applications, such as nonlinear resonances, change of vibration plane, coupling of rotational and translational motions etc. We also show how the geometry of suspension affects various dynamical effects and how an inverse problem may be formulated to enforce or diminish various dynamical effects. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=levitation" title="levitation">levitation</a>, <a href="https://publications.waset.org/abstracts/search?q=non-linear%20dynamics" title=" non-linear dynamics"> non-linear dynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=superconducting" title=" superconducting"> superconducting</a>, <a href="https://publications.waset.org/abstracts/search?q=diamagnetic%20stability" title=" diamagnetic stability "> diamagnetic stability </a> </p> <a href="https://publications.waset.org/abstracts/47249/modeling-and-controlling-nonlinear-dynamical-effects-in-non-contact-superconducting-and-diamagnetic-suspensions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/47249.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">410</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4954</span> Designing Intelligent Adaptive Controller for Nonlinear Pendulum Dynamical System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=R.%20Ghasemi">R. Ghasemi</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20R.%20Rahimi%20Khoygani"> M. R. Rahimi Khoygani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper proposes the designing direct adaptive neural controller to apply for a class of a nonlinear pendulum dynamic system. The radial basis function (RBF) neural adaptive controller is robust in presence of external and internal uncertainties. Both the effectiveness of the controller and robustness against disturbances are importance of this paper. The simulation results show the promising performance of the proposed controller. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adaptive%20neural%20controller" title="adaptive neural controller">adaptive neural controller</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20dynamical" title=" nonlinear dynamical"> nonlinear dynamical</a>, <a href="https://publications.waset.org/abstracts/search?q=neural%20network" title=" neural network"> neural network</a>, <a href="https://publications.waset.org/abstracts/search?q=RBF" title=" RBF"> RBF</a>, <a href="https://publications.waset.org/abstracts/search?q=driven%20pendulum" title=" driven pendulum"> driven pendulum</a>, <a href="https://publications.waset.org/abstracts/search?q=position%20control" title=" position control "> position control </a> </p> <a href="https://publications.waset.org/abstracts/13745/designing-intelligent-adaptive-controller-for-nonlinear-pendulum-dynamical-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/13745.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">482</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4953</span> Model-Free Distributed Control of Dynamical Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Javad%20Khazaei">Javad Khazaei</a>, <a href="https://publications.waset.org/abstracts/search?q=Rick%20Blum"> Rick Blum</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Distributed control is an efficient and flexible approach for coordination of multi-agent systems. One of the main challenges in designing a distributed controller is identifying the governing dynamics of the dynamical systems. Data-driven system identification is currently undergoing a revolution. With the availability of high-fidelity measurements and historical data, model-free identification of dynamical systems can facilitate the control design without tedious modeling of high-dimensional and/or nonlinear systems. This paper develops a distributed control design using consensus theory for linear and nonlinear dynamical systems using sparse identification of system dynamics. Compared with existing consensus designs that heavily rely on knowing the detailed system dynamics, the proposed model-free design can accurately capture the dynamics of the system with available measurements and input data and provide guaranteed performance in consensus and tracking problems. Heterogeneous damped oscillators are chosen as examples of dynamical system for validation purposes. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=consensus%20tracking" title="consensus tracking">consensus tracking</a>, <a href="https://publications.waset.org/abstracts/search?q=distributed%20control" title=" distributed control"> distributed control</a>, <a href="https://publications.waset.org/abstracts/search?q=model-free%20control" title=" model-free control"> model-free control</a>, <a href="https://publications.waset.org/abstracts/search?q=sparse%20identification%20of%20dynamical%20systems" title=" sparse identification of dynamical systems"> sparse identification of dynamical systems</a> </p> <a href="https://publications.waset.org/abstracts/144452/model-free-distributed-control-of-dynamical-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/144452.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">265</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4952</span> An Effective Modification to Multiscale Elastic Network Model and Its Evaluation Based on Analyses of Protein Dynamics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Weikang%20Gong">Weikang Gong</a>, <a href="https://publications.waset.org/abstracts/search?q=Chunhua%20Li"> Chunhua Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Dynamics plays an essential role in function exertion of proteins. Elastic network model (ENM), a harmonic potential-based and cost-effective computational method, is a valuable and efficient tool for characterizing the intrinsic dynamical properties encoded in biomacromolecule structures and has been widely used to detect the large-amplitude collective motions of proteins. Gaussian network model (GNM) and anisotropic network model (ANM) are the two often-used ENM models. In recent years, many ENM variants have been proposed. Here, we propose a small but effective modification (denoted as modified mENM) to the multiscale ENM (mENM) where fitting weights of Kirchhoff/Hessian matrixes with the least square method (LSM) is modified since it neglects the details of pairwise interactions. Then we perform its comparisons with the original mENM, traditional ENM, and parameter-free ENM (pfENM) on reproducing dynamical properties for the six representative proteins whose molecular dynamics (MD) trajectories are available in http://mmb.pcb.ub.es/MoDEL/. In the results, for B-factor prediction, mENM achieves the best performance among the four ENM models. Additionally, it is noted that with the weights of the multiscale Kirchhoff/Hessian matrixes modified, interestingly, the modified mGNM/mANM still has a much better performance than the corresponding traditional ENM and pfENM models. As to dynamical cross-correlation map (DCCM) calculation, taking the data obtained from MD trajectories as the standard, mENM performs the worst while the results produced by the modified mENM and pfENM models are close to those from MD trajectories with the latter a little better than the former. Generally, ANMs perform better than the corresponding GNMs except for the mENM. Thus, pfANM and the modified mANM, especially the former, have an excellent performance in dynamical cross-correlation calculation. Compared with GNMs (except for mGNM), the corresponding ANMs can capture quite a number of positive correlations for the residue pairs nearly largest distances apart, which is maybe due to the anisotropy consideration in ANMs. Furtherly, encouragingly the modified mANM displays the best performance in capturing the functional motional modes, followed by pfANM and traditional ANM models, while mANM fails in all the cases. This suggests that the consideration of long-range interactions is critical for ANM models to produce protein functional motions. Based on the analyses, the modified mENM is a promising method in capturing multiple dynamical characteristics encoded in protein structures. This work is helpful for strengthening the understanding of the elastic network model and provides a valuable guide for researchers to utilize the model to explore protein dynamics. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=elastic%20network%20model" title="elastic network model">elastic network model</a>, <a href="https://publications.waset.org/abstracts/search?q=ENM" title=" ENM"> ENM</a>, <a href="https://publications.waset.org/abstracts/search?q=multiscale%20ENM" title=" multiscale ENM"> multiscale ENM</a>, <a href="https://publications.waset.org/abstracts/search?q=molecular%20dynamics" title=" molecular dynamics"> molecular dynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=parameter-free%20ENM" title=" parameter-free ENM"> parameter-free ENM</a>, <a href="https://publications.waset.org/abstracts/search?q=protein%20structure" title=" protein structure"> protein structure</a> </p> <a href="https://publications.waset.org/abstracts/127143/an-effective-modification-to-multiscale-elastic-network-model-and-its-evaluation-based-on-analyses-of-protein-dynamics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/127143.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">121</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4951</span> On the Topological Entropy of Nonlinear Dynamical Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Graziano%20Chesi">Graziano Chesi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The topological entropy plays a key role in linear dynamical systems, allowing one to establish the existence of stabilizing feedback controllers for linear systems in the presence of communications constraints. This paper addresses the determination of a robust value of the topological entropy in nonlinear dynamical systems, specifically the largest value of the topological entropy over all linearized models in a region of interest of the state space. It is shown that a sufficient condition for establishing upper bounds of the sought robust value of the topological entropy can be given in terms of a semidefinite program (SDP), which belongs to the class of convex optimization problems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-linear%20system" title="non-linear system">non-linear system</a>, <a href="https://publications.waset.org/abstracts/search?q=communication%20constraint" title=" communication constraint"> communication constraint</a>, <a href="https://publications.waset.org/abstracts/search?q=topological%20entropy" title=" topological entropy"> topological entropy</a> </p> <a href="https://publications.waset.org/abstracts/45742/on-the-topological-entropy-of-nonlinear-dynamical-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/45742.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">323</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4950</span> Investigation on Performance of Change Point Algorithm in Time Series Dynamical Regimes and Effect of Data Characteristics </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Farhad%20Asadi">Farhad Asadi</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Javad%20Mollakazemi"> Mohammad Javad Mollakazemi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, Bayesian online inference in models of data series are constructed by change-points algorithm, which separated the observed time series into independent series and study the change and variation of the regime of the data with related statistical characteristics. variation of statistical characteristics of time series data often represent separated phenomena in the some dynamical system, like a change in state of brain dynamical reﬂected in EEG signal data measurement or a change in important regime of data in many dynamical system. In this paper, prediction algorithm for studying change point location in some time series data is simulated. It is verified that pattern of proposed distribution of data has important factor on simpler and smother fluctuation of hazard rate parameter and also for better identification of change point locations. Finally, the conditions of how the time series distribution effect on factors in this approach are explained and validated with different time series databases for some dynamical system. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=time%20series" title="time series">time series</a>, <a href="https://publications.waset.org/abstracts/search?q=fluctuation%20in%20statistical%20characteristics" title=" fluctuation in statistical characteristics"> fluctuation in statistical characteristics</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20learning" title=" optimal learning"> optimal learning</a>, <a href="https://publications.waset.org/abstracts/search?q=change-point%20algorithm" title=" change-point algorithm"> change-point algorithm</a> </p> <a href="https://publications.waset.org/abstracts/18167/investigation-on-performance-of-change-point-algorithm-in-time-series-dynamical-regimes-and-effect-of-data-characteristics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/18167.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">426</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4949</span> X-Ray Dynamical Diffraction 'Third Order Nonlinear Renninger Effect'</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Minas%20Balyan">Minas Balyan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Nowadays X-ray nonlinear diffraction and nonlinear effects are investigated due to the presence of the third generation synchrotron sources and XFELs. X-ray third order nonlinear dynamical diffraction is considered as well. Using the nonlinear model of the usual visible light optics the third-order nonlinear Takagi’s equations for monochromatic waves and the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses are obtained by the author in previous papers. The obtained equations show, that even if the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero (forbidden reflection), the dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus, in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well-known Renninger effect takes place. In this work, the 'third order nonlinear Renninger effect' is considered theoretically. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bragg%20diffraction" title="Bragg diffraction">Bragg diffraction</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20Takagi%E2%80%99s%20equations" title=" nonlinear Takagi’s equations"> nonlinear Takagi’s equations</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20Renninger%20effect" title=" nonlinear Renninger effect"> nonlinear Renninger effect</a>, <a href="https://publications.waset.org/abstracts/search?q=third%20order%20nonlinearity" title=" third order nonlinearity"> third order nonlinearity</a> </p> <a href="https://publications.waset.org/abstracts/55035/x-ray-dynamical-diffraction-third-order-nonlinear-renninger-effect" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/55035.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">385</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4948</span> Time-Evolving Wave Packet in Phase Space</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mitsuyoshi%20Tomiya">Mitsuyoshi Tomiya</a>, <a href="https://publications.waset.org/abstracts/search?q=Kentaro%20Kawamura"> Kentaro Kawamura</a>, <a href="https://publications.waset.org/abstracts/search?q=Shoichi%20Sakamoto"> Shoichi Sakamoto</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In chaotic billiard systems, scar-like localization has been found on time-evolving wave packet. We may call it the “dynamical scar” to separate it to the original scar in stationary states. It also comes out along the vicinity of classical unstable periodic orbits, when the wave packets are launched along the orbits, against the hypothesis that the waves become homogenous all around the billiard. Then time-evolving wave packets are investigated numerically in phase space. The Wigner function is adopted to detect the wave packets in phase space. The 2-dimensional Poincaré sections of the 4-dimensional phase space are introduced to clarify the dynamical behavior of the wave packets. The Poincaré sections of the coordinate (x or y) and the momentum (Px or Py) can visualize the dynamical behavior of the wave packets, including the behavior in the momentum degree also. For example, in “dynamical scar” states, a bit larger momentum component comes first, and then the a bit smaller and smaller components follow next. The sections made in the momentum space (Px or Py) elucidates specific trajectories that have larger contribution to the “dynamical scar” states. It is the fixed point observation of the momentum degrees at a specific fixed point(x0, y0) in the phase space. The accumulation are also calculated to search the “dynamical scar” in the Poincare sections. It is found the scars as bright spots in momentum degrees of the phase space. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=chaotic%20billiard" title="chaotic billiard">chaotic billiard</a>, <a href="https://publications.waset.org/abstracts/search?q=Poincar%C3%A9%20section" title=" Poincaré section"> Poincaré section</a>, <a href="https://publications.waset.org/abstracts/search?q=scar" title=" scar"> scar</a>, <a href="https://publications.waset.org/abstracts/search?q=wave%20packet" title=" wave packet"> wave packet</a> </p> <a href="https://publications.waset.org/abstracts/32869/time-evolving-wave-packet-in-phase-space" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32869.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">452</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4947</span> Dynamical Heterogeneity and Aging in Turbulence with a Nambu-Goldstone Mode</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fahrudin%20Nugroho">Fahrudin Nugroho</a>, <a href="https://publications.waset.org/abstracts/search?q=Halim%20Hamadi"> Halim Hamadi</a>, <a href="https://publications.waset.org/abstracts/search?q=Yusril%20Yusuf"> Yusril Yusuf</a>, <a href="https://publications.waset.org/abstracts/search?q=Pekik%20Nurwantoro"> Pekik Nurwantoro</a>, <a href="https://publications.waset.org/abstracts/search?q=Ari%20Setiawan"> Ari Setiawan</a>, <a href="https://publications.waset.org/abstracts/search?q=Yoshiki%20Hidaka"> Yoshiki Hidaka</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We investigate the Nikolaevskiy equation numerically using exponential time differencing method and pseudo-spectral method. This equation develops a long-wavelength modulation that behaves as a Nambu–Goldstone mode, and short-wavelength instability and exhibit turbulence. Using the autocorrelation analysis, the statistical properties of the turbulence governed by the equation are investigated. The autocorrelation then has been fitted with The Kohlrausch– Williams–Watts (KWW) expression. By varying the control parameter, we show a transition from compressed to stretched exponential for the auto-correlation function of Nikolaevskiy turbulence. The compressed exponential is an indicator of the existence of dynamical heterogeneity while the stretched indicates aging process. Thereby, we revealed the existence of dynamical heterogeneity and aging in the turbulence governed by Nikolaevskiy equation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=compressed%20exponential" title="compressed exponential">compressed exponential</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamical%20heterogeneity" title=" dynamical heterogeneity"> dynamical heterogeneity</a>, <a href="https://publications.waset.org/abstracts/search?q=Nikolaevskiy%20equation" title=" Nikolaevskiy equation"> Nikolaevskiy equation</a>, <a href="https://publications.waset.org/abstracts/search?q=stretched%20exponential" title=" stretched exponential"> stretched exponential</a>, <a href="https://publications.waset.org/abstracts/search?q=turbulence" title=" turbulence"> turbulence</a> </p> <a href="https://publications.waset.org/abstracts/48908/dynamical-heterogeneity-and-aging-in-turbulence-with-a-nambu-goldstone-mode" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48908.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">436</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4946</span> Quantum Localization of Vibrational Mirror in Cavity Optomechanics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Madiha%20Tariq">Madiha Tariq</a>, <a href="https://publications.waset.org/abstracts/search?q=Hena%20Rabbani"> Hena Rabbani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Recently, cavity-optomechanics becomes an extensive research field that has manipulated the mechanical effects of light for coupling of the optical field with other physical objects specifically with regards to dynamical localization. We investigate the dynamical localization (both in momentum and position space) for a vibrational mirror in a Fabry-Pérot cavity driven by a single mode optical field and a transverse probe field. The weak probe field phenomenon results in classical chaos in phase space and spatio temporal dynamics in position |ψ(x)²| and momentum space |ψ(p)²| versus time show quantum localization in both momentum and position space. Also, we discuss the parametric dependencies of dynamical localization for a designated set of parameters to be experimentally feasible. Our work opens an avenue to manipulate the other optical phenomena and applicability of proposed work can be prolonged to turn-able laser sources in the future. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dynamical%20localization" title="dynamical localization">dynamical localization</a>, <a href="https://publications.waset.org/abstracts/search?q=cavity%20optomechanics" title=" cavity optomechanics"> cavity optomechanics</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamiltonian%20chaos" title=" Hamiltonian chaos"> Hamiltonian chaos</a>, <a href="https://publications.waset.org/abstracts/search?q=probe%20field" title=" probe field"> probe field</a> </p> <a href="https://publications.waset.org/abstracts/108127/quantum-localization-of-vibrational-mirror-in-cavity-optomechanics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/108127.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">150</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4945</span> Calculating Non-Unique Sliding Modes for Switched Dynamical Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Eugene%20Stepanov">Eugene Stepanov</a>, <a href="https://publications.waset.org/abstracts/search?q=Arkadi%20Ponossov"> Arkadi Ponossov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Ordinary differential equations with switching nonlinearities constitute a very useful tool in many applications. The solutions of such equations can usually be calculated analytically if they cross the discontinuities transversally. Otherwise, one has trajectories that slides along the discontinuity, and the calculations become less straightforward in this case. For instance, one of the problems one faces is non-uniqueness of the sliding modes. In the presentation, it is proposed to apply the theory of hybrid dynamical systems to calculate the solutions that are ‘hidden’ in the discontinuities. Roughly, one equips the underlying switched system with an explicitly designed discrete dynamical system (‘automaton’), which governs the dynamics of the switched system. This construction ‘splits’ the dynamics, which, as it is shown in the presentation, gives uniqueness of the resulting hybrid trajectories and at the same time provides explicit formulae for them. Projecting the hybrid trajectories back onto the original continuous system explains non-uniqueness of its trajectories. The automaton is designed with the help of the attractors of the specially constructed adjoint dynamical system. Several examples are provided in the presentation, which supports the efficiency of the suggested scheme. The method can be of interest in control theory, gene regulatory networks, neural field models and other fields, where switched dynamics is a part of the analysis. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hybrid%20dynamical%20systems" title="hybrid dynamical systems">hybrid dynamical systems</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20perturbation%20analysis" title=" singular perturbation analysis"> singular perturbation analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=sliding%20modes" title=" sliding modes"> sliding modes</a>, <a href="https://publications.waset.org/abstracts/search?q=switched%20dynamics" title=" switched dynamics"> switched dynamics</a> </p> <a href="https://publications.waset.org/abstracts/86304/calculating-non-unique-sliding-modes-for-switched-dynamical-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/86304.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">163</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4944</span> Efficient Neural and Fuzzy Models for the Identification of Dynamical Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Aouiche%20Abdelaziz">Aouiche Abdelaziz</a>, <a href="https://publications.waset.org/abstracts/search?q=Soudani%20Mouhamed%20Salah"> Soudani Mouhamed Salah</a>, <a href="https://publications.waset.org/abstracts/search?q=Aouiche%20El%20Moundhe"> Aouiche El Moundhe</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The present paper addresses the utilization of Artificial Neural Networks (ANNs) and Fuzzy Inference Systems (FISs) for the identification and control of dynamical systems with some degree of uncertainty. Because ANNs and FISs have an inherent ability to approximate functions and to adapt to changes in input and parameters, they can be used to control systems too complex for linear controllers. In this work, we show how ANNs and FISs can be put in order to form nets that can learn from external data. In sequence, it is presented structures of inputs that can be used along with ANNs and FISs to model non-linear systems. Four systems were used to test the identification and control of the structures proposed. The results show the ANNs and FISs (Back Propagation Algorithm) used were efficient in modeling and controlling the non-linear plants. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-linear%20systems" title="non-linear systems">non-linear systems</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20set%20Models" title=" fuzzy set Models"> fuzzy set Models</a>, <a href="https://publications.waset.org/abstracts/search?q=neural%20network" title=" neural network"> neural network</a>, <a href="https://publications.waset.org/abstracts/search?q=control%20law" title=" control law"> control law</a> </p> <a href="https://publications.waset.org/abstracts/142525/efficient-neural-and-fuzzy-models-for-the-identification-of-dynamical-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/142525.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">212</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4943</span> Increase in the Persistence of Various Invaded Multiplex Metacommunities Induced by Heterogeneity of Motifs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Dweepabiswa%20Bagchi">Dweepabiswa Bagchi</a>, <a href="https://publications.waset.org/abstracts/search?q=D.%20V.%20Senthilkumar"> D. V. Senthilkumar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Numerous studies have typically demonstrated the devastation of invasions on an isolated ecosystem or, at most, a network of dispersively coupled similar ecosystem patches. Using such a simplistic 2-D network model, one can only consider dispersal coupling and inter-species trophic interactions. However, in a realistic ecosystem, numerous species co-exist and interact trophically and non-trophically in groups of 2 or more. Even different types of dispersal can introduce complexity in an ecological network. Therefore, a more accurate representation of actual ecosystems (or ecological networks) is a complex network consisting of motifs formed by two or more interacting species. Here, the apropos structure of the network should be multiplex or multi-layered. Motifs between different patches or species should be identical within the same layer and vary from one layer to another. This study investigates three distinct ecological multiplex networks facing invasion from one or more external species. This work determines and quantifies the criteria for the increased extinction risk of these networks. The dynamical states of the network with high extinction risk, i.e., the danger states, and those with low extinction risk, i.e., the resistive network states, are both subsequently identified. The analysis done in this study further quantifies the persistence of the entire network corresponding to simultaneous changes in the strength of invasive dispersal and higher-order trophic and non-trophic interactions. This study also demonstrates that the ecosystems enjoy an inherent advantage against invasions due to their multiplex network structure. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=increased%20ecosystem%20persistence" title="increased ecosystem persistence">increased ecosystem persistence</a>, <a href="https://publications.waset.org/abstracts/search?q=invasion%20on%20ecosystems" title=" invasion on ecosystems"> invasion on ecosystems</a>, <a href="https://publications.waset.org/abstracts/search?q=multiplex%20networks" title=" multiplex networks"> multiplex networks</a>, <a href="https://publications.waset.org/abstracts/search?q=non-trophic%20interactions" title=" non-trophic interactions"> non-trophic interactions</a> </p> <a href="https://publications.waset.org/abstracts/176495/increase-in-the-persistence-of-various-invaded-multiplex-metacommunities-induced-by-heterogeneity-of-motifs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/176495.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">64</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4942</span> X-Ray Dynamical Diffraction Rocking Curves in Case of Third Order Nonlinear Renninger Effect</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Minas%20Balyan">Minas Balyan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the third-order nonlinear Takagi’s equations for monochromatic waves and in the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses for forbidden reflections the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero. The dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well known Renninger effect takes place. In this work, the ‘third order nonlinear Renninger effect’ is considered theoretically and numerically. If the reflection exactly is forbidden the diffracted wave’s amplitude is zero both in Laue and Bragg cases since the boundary conditions and dynamical diffraction equations are compatible with zero solution. But in real crystals due to some percent of dislocations and other localized defects, the atoms are displaced with respect to their equilibrium positions. Thus in real crystals susceptibilities of forbidden reflection are by some order small than for usual not forbidden reflections but are not exactly equal to zero. The numerical calculations for susceptibilities two order less than for not forbidden reflection show that in Bragg geometry case the nonlinear reflection curve’s behavior is the same as for not forbidden reflection, but for forbidden reflection the rocking curves’ width, center and boundaries are two order sensitive on the input intensity value. This gives an opportunity to investigate third order nonlinear X-ray dynamical diffraction for not intense beams – 0.001 in the units of critical intensity. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=third%20order%20nonlinearity" title="third order nonlinearity">third order nonlinearity</a>, <a href="https://publications.waset.org/abstracts/search?q=Bragg%20diffraction" title=" Bragg diffraction"> Bragg diffraction</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20Renninger%20effect" title=" nonlinear Renninger effect"> nonlinear Renninger effect</a>, <a href="https://publications.waset.org/abstracts/search?q=rocking%20curves" title=" rocking curves"> rocking curves</a> </p> <a href="https://publications.waset.org/abstracts/56984/x-ray-dynamical-diffraction-rocking-curves-in-case-of-third-order-nonlinear-renninger-effect" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/56984.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">406</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4941</span> Experimental Networks Synchronization of Chua’s Circuit in Different Topologies</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Manuel%20Meranza-Castillon">Manuel Meranza-Castillon</a>, <a href="https://publications.waset.org/abstracts/search?q=Rolando%20Diaz-Castillo"> Rolando Diaz-Castillo</a>, <a href="https://publications.waset.org/abstracts/search?q=Adrian%20Arellano-Delgado"> Adrian Arellano-Delgado</a>, <a href="https://publications.waset.org/abstracts/search?q=Cesar%20Cruz-Hernandez"> Cesar Cruz-Hernandez</a>, <a href="https://publications.waset.org/abstracts/search?q=Rosa%20Martha%20Lopez-Gutierrez"> Rosa Martha Lopez-Gutierrez</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we deal with experimental network synchronization of chaotic nodes with different topologies. Our approach is based on complex system theory, and we use a master-slave configuration to couple the nodes in the networks. In particular, we design and implement electronically complex dynamical networks composed by nine coupled chaotic Chua’s circuits with topologies: in nearest-neighbor, small-world, open ring, star, and global. Also, network synchronization is evaluated according to a particular coupling strength for each topology. This study is important by the possible applications to private transmission of information in a chaotic communication network of multiple users. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=complex%20networks" title="complex networks">complex networks</a>, <a href="https://publications.waset.org/abstracts/search?q=Chua%27s%20circuit" title=" Chua's circuit"> Chua's circuit</a>, <a href="https://publications.waset.org/abstracts/search?q=experimental%20synchronization" title=" experimental synchronization"> experimental synchronization</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple%20users" title=" multiple users"> multiple users</a> </p> <a href="https://publications.waset.org/abstracts/64455/experimental-networks-synchronization-of-chuas-circuit-in-different-topologies" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/64455.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">348</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4940</span> Finite Time Blow-Up and Global Solutions for a Semilinear Parabolic Equation with Linear Dynamical Boundary Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Xu%20Runzhang">Xu Runzhang</a>, <a href="https://publications.waset.org/abstracts/search?q=Yang%20Yanbing"> Yang Yanbing</a>, <a href="https://publications.waset.org/abstracts/search?q=Niu%20Yi"> Niu Yi</a>, <a href="https://publications.waset.org/abstracts/search?q=Zhang%20Mingyou"> Zhang Mingyou</a>, <a href="https://publications.waset.org/abstracts/search?q=Liu%20Yu"> Liu Yu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> For a class of semilinear parabolic equations with linear dynamical boundary conditions in a bounded domain, we obtain both global solutions and finite time blow-up solutions when the initial data varies in the phase space H1(Ω). Our main tools are the comparison principle, the potential well method and the concavity method. In particular, we discuss the behavior of the solutions with the initial data at critical and high energy level. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=high%20energy%20level" title="high energy level">high energy level</a>, <a href="https://publications.waset.org/abstracts/search?q=critical%20energy%20level" title=" critical energy level"> critical energy level</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20dynamical%20boundary%20condition" title=" linear dynamical boundary condition"> linear dynamical boundary condition</a>, <a href="https://publications.waset.org/abstracts/search?q=semilinear%20parabolic%20equation" title=" semilinear parabolic equation"> semilinear parabolic equation</a> </p> <a href="https://publications.waset.org/abstracts/24012/finite-time-blow-up-and-global-solutions-for-a-semilinear-parabolic-equation-with-linear-dynamical-boundary-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/24012.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">436</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4939</span> Periodically Forced Oscillator with Noisy Chaotic Dynamics </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Adedayo%20Oke%20Adelakun">Adedayo Oke Adelakun</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The chaotic dynamics of periodically forced oscillators with smooth potential has been extensively investigated via theoretical, numerical and experimental simulations. With the advent of the study of chaotic dynamics by means of method of multiple time scale analysis, Melnikov theory, bifurcation diagram, Poincare's map, bifurcation diagrams and Lyapunov exponents, it has become necessary to seek for a better understanding of nonlinear oscillator with noisy term. In this paper, we examine the influence of noise on complex dynamical behaviour of periodically forced F6 - Duffing oscillator for specific choice of noisy parameters. The inclusion of noisy term improves the dynamical behaviour of the oscillator which may have wider application in secure communication than smooth potential. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hierarchical%20structure" title="hierarchical structure">hierarchical structure</a>, <a href="https://publications.waset.org/abstracts/search?q=periodically%20forced%20oscillator" title=" periodically forced oscillator"> periodically forced oscillator</a>, <a href="https://publications.waset.org/abstracts/search?q=noisy%20parameters" title=" noisy parameters"> noisy parameters</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamical%20behaviour" title=" dynamical behaviour"> dynamical behaviour</a>, <a href="https://publications.waset.org/abstracts/search?q=F6%20-%20duffing%20oscillator" title=" F6 - duffing oscillator"> F6 - duffing oscillator</a> </p> <a href="https://publications.waset.org/abstracts/47494/periodically-forced-oscillator-with-noisy-chaotic-dynamics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/47494.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">325</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4938</span> Reconstruction and Rejection of External Disturbances in a Dynamical System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Iftikhar%20Ahmad">Iftikhar Ahmad</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Benallegue"> A. Benallegue</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20El%20Hadri"> A. El Hadri</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we have proposed an observer for the reconstruction and a control law for the rejection application of unknown bounded external disturbance in a dynamical system. The strategy of both the observer and the controller is designed like a second order sliding mode with a proportional-integral (PI) term. Lyapunov theory is used to prove the exponential convergence and stability. Simulations results are given to show the performance of this method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-linear%20systems" title="non-linear systems">non-linear systems</a>, <a href="https://publications.waset.org/abstracts/search?q=sliding%20mode%20observer" title=" sliding mode observer"> sliding mode observer</a>, <a href="https://publications.waset.org/abstracts/search?q=disturbance%20rejection" title=" disturbance rejection"> disturbance rejection</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20control" title=" nonlinear control"> nonlinear control</a> </p> <a href="https://publications.waset.org/abstracts/44910/reconstruction-and-rejection-of-external-disturbances-in-a-dynamical-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/44910.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">334</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4937</span> Solving Ill-Posed Initial Value Problems for Switched Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Eugene%20Stepanov">Eugene Stepanov</a>, <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov"> Arcady Ponosov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> To model gene regulatory networks one uses ordinary differential equations with switching nonlinearities, where the initial value problem is known to be well-posed if the trajectories cross the discontinuities transversally. Otherwise, the initial value problem is usually ill-posed, which lead to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid dynamical systems, rather than switched ones, to regularize the problem. 'Hybridization' of the switched system means that one attaches a dynamic discrete component ('automaton'), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness of the initial value problem making it well-posed. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. Several examples are provided in the presentation, which support the suggested analysis. The method can also be of interest in other applied fields, where differential equations contain switchings, e.g. in neural field models. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hybrid%20dynamical%20systems" title="hybrid dynamical systems">hybrid dynamical systems</a>, <a href="https://publications.waset.org/abstracts/search?q=ill-posed%20problems" title=" ill-posed problems"> ill-posed problems</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20perturbation%20analysis" title=" singular perturbation analysis"> singular perturbation analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=switching%20nonlinearities" title=" switching nonlinearities"> switching nonlinearities</a> </p> <a href="https://publications.waset.org/abstracts/85884/solving-ill-posed-initial-value-problems-for-switched-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/85884.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">184</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4936</span> Chaos Analysis of a 3D Finance System and Generalized Synchronization for N-Dimension</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muhammad%20Fiaz">Muhammad Fiaz</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The article in hand is the study of complex features like Zero Hopf Bifurcation, Chaos and Synchronization of integer and fractional order version of a new 3D finance system. Trusted tools of averaging theory and active control method are utilized for investigation of Zero Hopf bifurcation and synchronization for both versions respectively. Inventiveness of the paper is to find the answer of a question that is it possible to find a chaotic system which can be synchronized with any other of the same dimension? Based on different examples we categorically develop a theory that if a couple of master and slave chaotic dynamical system is synchronized by selecting a suitable gain matrix with special conditions then the master system is synchronized with any chaotic dynamical system of the same dimension. With the help of this study we developed generalized theorems for synchronization of n-dimension dynamical systems for integer as well as fractional versions. it proposed that this investigation will contribute a lot to control dynamical systems and only a suitable gain matrix with special conditions is enough to synchronize the system under consideration with any other chaotic system of the same dimension. Chaotic properties of fractional version of the new finance system are also analyzed at fractional order q=0.87. Simulations results, where required, also provided for authenticity of analytical study. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=complex%20analysis" title="complex analysis">complex analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=chaos" title=" chaos"> chaos</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20synchronization" title=" generalized synchronization"> generalized synchronization</a>, <a href="https://publications.waset.org/abstracts/search?q=control%20dynamics" title=" control dynamics"> control dynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20order%20analysis" title=" fractional order analysis"> fractional order analysis</a> </p> <a href="https://publications.waset.org/abstracts/182892/chaos-analysis-of-a-3d-finance-system-and-generalized-synchronization-for-n-dimension" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/182892.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">68</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4935</span> Nonlinear Observer Canonical Form for Genetic Regulation Process</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bououden%20Soraya">Bououden Soraya</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper aims to study the existence of the change of coordinates which permits to transform a class of nonlinear dynamical systems into the so-called nonlinear observer canonical form (NOCF). Moreover, an algorithm to construct such a change of coordinates is given. Based on this form, we can design an observer with a linear error dynamic. This enables us to estimate the state of a nonlinear dynamical system. A concrete example (biological model) is provided to illustrate the feasibility of the proposed results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20observer%20canonical%20form" title="nonlinear observer canonical form">nonlinear observer canonical form</a>, <a href="https://publications.waset.org/abstracts/search?q=observer" title=" observer"> observer</a>, <a href="https://publications.waset.org/abstracts/search?q=design" title=" design"> design</a>, <a href="https://publications.waset.org/abstracts/search?q=gene%20regulation" title=" gene regulation"> gene regulation</a>, <a href="https://publications.waset.org/abstracts/search?q=gene%20expression" title=" gene expression"> gene expression</a> </p> <a href="https://publications.waset.org/abstracts/37920/nonlinear-observer-canonical-form-for-genetic-regulation-process" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37920.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">432</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4934</span> Feigenbaum Universality, Chaos and Fractal Dimensions in Discrete Dynamical Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=T.%20K.%20Dutta">T. K. Dutta</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20K.%20Das"> K. K. Das</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20Dutta"> N. Dutta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The salient feature of this paper is primarily concerned with Ricker’s population model: f(x)=x e^(r(1-x/k)), where r is the control parameter and k is the carrying capacity, and some fruitful results are obtained with the following objectives: 1) Determination of bifurcation values leading to a chaotic region, 2) Development of Statistical Methods and Analysis required for the measure of Fractal dimensions, 3) Calculation of various fractal dimensions. These results also help that the invariant probability distribution on the attractor, when it exists, provides detailed information about the long-term behavior of a dynamical system. At the end, some open problems are posed for further research. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Feigenbaum%20universality" title="Feigenbaum universality">Feigenbaum universality</a>, <a href="https://publications.waset.org/abstracts/search?q=chaos" title=" chaos"> chaos</a>, <a href="https://publications.waset.org/abstracts/search?q=Lyapunov%20exponent" title=" Lyapunov exponent"> Lyapunov exponent</a>, <a href="https://publications.waset.org/abstracts/search?q=fractal%20dimensions" title=" fractal dimensions"> fractal dimensions</a> </p> <a href="https://publications.waset.org/abstracts/4761/feigenbaum-universality-chaos-and-fractal-dimensions-in-discrete-dynamical-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4761.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">302</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4933</span> Fractal Analysis of Some Bifurcations of Discrete Dynamical Systems in Higher Dimensions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lana%20Horvat%20Dmitrovi%C4%87">Lana Horvat Dmitrović</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The main purpose of this paper is to study the box dimension as fractal property of bifurcations of discrete dynamical systems in higher dimensions. The paper contains the fractal analysis of the orbits near the hyperbolic and non-hyperbolic fixed points in discrete dynamical systems. It is already known that in one-dimensional case the orbit near the hyperbolic fixed point has the box dimension equal to zero. On the other hand, the orbit near the non-hyperbolic fixed point has strictly positive box dimension which is connected to the non-degeneracy condition of certain bifurcation. One of the main results in this paper is the generalisation of results about box dimension near the hyperbolic and non-hyperbolic fixed points to higher dimensions. In the process of determining box dimension, the restriction of systems to stable, unstable and center manifolds, Lipschitz property of box dimension and the notion of projective box dimension are used. The analysis of the bifurcations in higher dimensions with one multiplier on the unit circle is done by using the normal forms on one-dimensional center manifolds. This specific change in box dimension of an orbit at the moment of bifurcation has already been explored for some bifurcations in one and two dimensions. It was shown that specific values of box dimension are connected to appropriate bifurcations such as fold, flip, cusp or Neimark-Sacker bifurcation. This paper further explores this connection of box dimension as fractal property to some specific bifurcations in higher dimensions, such as fold-flip and flip-Neimark-Sacker. Furthermore, the application of the results to the unit time map of continuous dynamical system near hyperbolic and non-hyperbolic singularities is presented. In that way, box dimensions which are specific for certain bifurcations of continuous systems can be obtained. The approach to bifurcation analysis by using the box dimension as specific fractal property of orbits can lead to better understanding of bifurcation phenomenon. It could also be useful in detecting the existence or nonexistence of bifurcations of discrete and continuous dynamical systems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bifurcation" title="bifurcation">bifurcation</a>, <a href="https://publications.waset.org/abstracts/search?q=box%20dimension" title=" box dimension"> box dimension</a>, <a href="https://publications.waset.org/abstracts/search?q=invariant%20manifold" title=" invariant manifold"> invariant manifold</a>, <a href="https://publications.waset.org/abstracts/search?q=orbit%20near%20fixed%20point" title=" orbit near fixed point"> orbit near fixed point</a> </p> <a href="https://publications.waset.org/abstracts/52891/fractal-analysis-of-some-bifurcations-of-discrete-dynamical-systems-in-higher-dimensions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52891.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">254</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4932</span> Parameter Estimation in Dynamical Systems Based on Latent Variables</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov">Arcady Ponosov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A novel mathematical approach is suggested, which facilitates a compressed representation and efficient validation of parameter-rich ordinary differential equation models describing the dynamics of complex, especially biology-related, systems and which is based on identification of the system's latent variables. In particular, an efficient parameter estimation method for the compressed non-linear dynamical systems is developed. The method is applied to the so-called 'power-law systems' being non-linear differential equations typically used in Biochemical System Theory. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=generalized%20law%20of%20mass%20action" title="generalized law of mass action">generalized law of mass action</a>, <a href="https://publications.waset.org/abstracts/search?q=metamodels" title=" metamodels"> metamodels</a>, <a href="https://publications.waset.org/abstracts/search?q=principal%20components" title=" principal components"> principal components</a>, <a href="https://publications.waset.org/abstracts/search?q=synergetic%20systems" title=" synergetic systems"> synergetic systems</a> </p> <a href="https://publications.waset.org/abstracts/42041/parameter-estimation-in-dynamical-systems-based-on-latent-variables" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/42041.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">355</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4931</span> A Combined Error Control with Forward Euler Method for Dynamical Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=R.%20Vigneswaran">R. Vigneswaran</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Thilakanathan"> S. Thilakanathan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Variable time-stepping algorithms for solving dynamical systems performed poorly for long time computations which pass close to a fixed point. To overcome this difficulty, several authors considered phase space error controls for numerical simulation of dynamical systems. In one generalized phase space error control, a step-size selection scheme was proposed, which allows this error control to be incorporated into the standard adaptive algorithm as an extra constraint at negligible extra computational cost. For this generalized error control, it was already analyzed the forward Euler method applied to the linear system whose coefficient matrix has real and negative eigenvalues. In this paper, this result was extended to the linear system whose coefficient matrix has complex eigenvalues with negative real parts. Some theoretical results were obtained and numerical experiments were carried out to support the theoretical results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adaptivity" title="adaptivity">adaptivity</a>, <a href="https://publications.waset.org/abstracts/search?q=fixed%20point" title=" fixed point"> fixed point</a>, <a href="https://publications.waset.org/abstracts/search?q=long%20time%20simulations" title=" long time simulations"> long time simulations</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20system" title=" linear system"> linear system</a> </p> <a href="https://publications.waset.org/abstracts/48246/a-combined-error-control-with-forward-euler-method-for-dynamical-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48246.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">312</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4930</span> Some Results on Cluster Synchronization</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shahed%20Vahedi">Shahed Vahedi</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohd%20Salmi%20Md%20Noorani"> Mohd Salmi Md Noorani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper investigates cluster synchronization phenomena between community networks. We focus on the situation where a variety of dynamics occur in the clusters. In particular, we show that different synchronization states simultaneously occur between the networks. The controller is designed having an adaptive control gain, and theoretical results are derived via Lyapunov stability. Simulations on well-known dynamical systems are provided to elucidate our results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cluster%20synchronization" title="cluster synchronization">cluster synchronization</a>, <a href="https://publications.waset.org/abstracts/search?q=adaptive%20control" title=" adaptive control"> adaptive control</a>, <a href="https://publications.waset.org/abstracts/search?q=community%20network" title=" community network"> community network</a>, <a href="https://publications.waset.org/abstracts/search?q=simulation" title=" simulation"> simulation</a> </p> <a href="https://publications.waset.org/abstracts/28916/some-results-on-cluster-synchronization" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/28916.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 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