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Synchronization of chaotic nonlinear continuous neural networks with time-varying delay

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Abstract

In this paper, the synchronization problem for delayed continuous time nonlinear complex neural networks is considered. The delay dependent state feed back synchronization gain matrix is obtained by considering more general case of time-varying delay. Using Lyapunov stability theory, the sufficient synchronization criteria are derived in terms of Linear Matrix Inequalities (LMIs). By decomposing the delay interval into multiple equidistant subintervals, Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals. Employing these LKFs, new delay dependent synchronization criteria are proposed in terms of LMIs for two cases with and without derivative of time-varying delay. Numerical examples are illustrated to show the effectiveness of the proposed method.

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Acknowledgments

The research is supported by University Grant Commission, Government of India, under Faculty Development Programme, XI plan grant. The authors would like to thank the Editor-in-Chief and anonymous reviewers for their valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Gandhigram Rural Institute, Deemed University, Gandhigram, Tamilnadu, 624 302, India

    P. Balasubramaniam & S. Jeeva Sathya Theesar

  2. Department of Computer Science, Government Arts College, Melur, Madurai, Tamilnadu, 625 106, India

    R. Chandran

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  1. P. Balasubramaniam
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  2. R. Chandran
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  3. S. Jeeva Sathya Theesar
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Correspondence to P. Balasubramaniam.

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Balasubramaniam, P., Chandran, R. & Jeeva Sathya Theesar, S. Synchronization of chaotic nonlinear continuous neural networks with time-varying delay. Cogn Neurodyn 5, 361–371 (2011). https://doi.org/10.1007/s11571-011-9162-0

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  • DOI: https://doi.org/10.1007/s11571-011-9162-0

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