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Adaptive synchronization of the complex dynamical network with double non-delayed and double delayed coupling

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Abstract

To simulate more realistic networks, we introduce a complex dynamical network model with double non-delayed and double delayed coupling and further investigate its synchronization phenomenon in this paper. Based on Lyapunov stability theory, adaptive synchronization criteria is obtained. Analytical result shows that under the designed adaptive controllers, the complex dynamical network with double non-delayed and double delayed coupling can asymptotically synchronize to a given trajectory. What is more, the coupling matrix is not assumed to be symmetric or irreducible. Finally, simulation results show the method is effective.

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Authors and Affiliations

  1. College of Department of Mathematics and Finance, Yunyang Teachers’ College, Hubei, Shiyan, 442000, P. R. China

    Yuhua Xu

  2. College of Information Science and Technology, Donghua University, Shanghai, 201620, P. R. China

    Wuneng Zhou & Jian-an Fang

Authors
  1. Yuhua Xu
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  2. Wuneng Zhou
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  3. Jian-an Fang
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Corresponding author

Correspondence to Yuhua Xu.

Additional information

Recommended by Editorial Board member Hamid Reza Karimi under the direction of Editor Young Il Lee.

This work was supported by the National Natural Science Foundation of China (61075060), the Innovation Program of Shanghai Municipal Education Commission (12zz064), the Science and Technology Research Key Program for the Education Department of Hubei Province of China (D20105001, D20125001) and the Natural Science Foundation of Yunyang Teachers’College (2011A01).

Yuhua Xu received his Ph.D. degree in Control Theory and Control Engineering from Donghua University, P. R. China in 2011. Currently he is an Associate Professor at Yunyang Teachers’ College. His research interests include include robust control, chaos synchronization, network control.

Wuneng Zhou received his Ph.D. degree in Control Theory and Control Engineering from Zhejiang University, P. R. China in 2005. Currently he is a Professor at Donghua University. His research interests include robust control, chaos synchronization, network control, as well as analysis and control of complex stochastic systems.

Jian-an Fang received his M.Sc. and Ph.D. degrees in Control Theory and Control Engineering from Donghua University. His research interests include nonlinear control, adaptive control, complex system modeling, analysis and control, network control.

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Xu, Y., Zhou, W. & Fang, Ja. Adaptive synchronization of the complex dynamical network with double non-delayed and double delayed coupling. Int. J. Control Autom. Syst. 10, 415–420 (2012). https://doi.org/10.1007/s12555-012-0221-z

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  • DOI: https://doi.org/10.1007/s12555-012-0221-z

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