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Adaptive Cluster Synchronization for Nondelayed and Delayed Coupling Complex Networks with Nonidentical Nodes

Author

Listed:
  • Ze Tang
  • Jianwen Feng

Abstract

We focus on the cluster synchronization problem for a kind of general networks with nondelayed and delayed coupling. Based on the pinning control scheme, a small fraction of the nodes in each cluster are pinned for successful control, and the states of the whole dynamical networks can be globally forced to the objective cluster states. Sufficient conditions are derived to guarantee the realization of the cluster synchronization pattern for all initial values by means of the Lyapunov stability theorem and linear matrix inequalities (LMIs). By using the adaptive update law, relative smaller control gains are obtained, and hence the control cost can be substantially lower. Numerical simulations are also exploited to demonstrate the effectiveness and validity of the main result.

Suggested Citation

  • Ze Tang & Jianwen Feng, 2013. "Adaptive Cluster Synchronization for Nondelayed and Delayed Coupling Complex Networks with Nonidentical Nodes," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:946243
    DOI: 10.1155/2013/946243
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    References listed on IDEAS

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    1. Yu, Wenwu & Cao, Jinde, 2007. "Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 467-482.
    2. Yang Tang & Huijun Gao & Wei Zou & Jürgen Kurths, 2012. "Identifying Controlling Nodes in Neuronal Networks in Different Scales," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-13, July.
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