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Bidirectionally coupled synchronization of the generalized Lorenz systems

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Abstract

Wu, Chen, and Cai (2007) investigated chaos synchronization of two identical generalized Lorenz systems unidirectionally coupled by a linear state error feedback controller. However, bidirectional coupling in real life such as complex dynamical networks is more universal. This paper provides a unified method for analyzing chaos synchronization of two bidirectionally coupled generalized Lorenz systems. Some sufficient synchronization conditions for some special coupling matrices (diagonal matrices, so-called dislocated coupling matrices, and so on) are derived through rigorously mathematical theory. In particular, for the classical Lorenz system, the authors obtain synchronization criteria which only depend upon its parameters using new estimation of the ultimate bounds of Lorenz system (Chaos, Solitons, and Fractals, 2005). The criteria are then applied to four typical generalized Lorenz systems in the numerical simulations for verification.

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Juan Chen, Jun-an Lu & Xiaoqun Wu

Authors
  1. Juan Chen
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  2. Jun-an Lu
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  3. Xiaoqun Wu
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Corresponding author

Correspondence to Juan Chen.

Additional information

The research was supported by the National Natural Science Foundation of China under Grant Nos. 60804039 and 60974081, and the National Basic Research Program of China under Grant No. 2007CB310805.

This paper was recommended for publication by Editor Jinhu LÜ.

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Chen, J., Lu, Ja. & Wu, X. Bidirectionally coupled synchronization of the generalized Lorenz systems. J Syst Sci Complex 24, 433–448 (2011). https://doi.org/10.1007/s11424-010-8323-2

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  • DOI: https://doi.org/10.1007/s11424-010-8323-2

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