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A single adaptive controller with one variable for synchronizing two identical time delay hyperchaotic Lorenz systems with mismatched parameters

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Abstract

Time delays are ubiquitous in real world and are often sources of complex behaviors of dynamical systems. This paper addresses the problem of parameter identification and synchronization of uncertain hyperchaotic time-delayed systems. Based on the Lyapunov stability theory and the adaptive control theory, a single adaptive controller with one variable for synchronizing two identical time-delay hyperchaotic Lorenz systems with mismatch parameters is proposed. The parameter update laws and sufficient conditions of the scheme are obtained for both linear feedback and adaptive control approaches. Numerical simulations are also given to show the effectiveness of the proposed method.

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Authors and Affiliations

  1. School of Mathematical Sciences, Yancheng Teachers University, Yancheng, 224002, China

    Xuerong Shi & Zuolei Wang

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  1. Xuerong Shi
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  2. Zuolei Wang
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Correspondence to Xuerong Shi.

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Shi, X., Wang, Z. A single adaptive controller with one variable for synchronizing two identical time delay hyperchaotic Lorenz systems with mismatched parameters. Nonlinear Dyn 69, 117–125 (2012). https://doi.org/10.1007/s11071-011-0250-9

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  • DOI: https://doi.org/10.1007/s11071-011-0250-9

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