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Complex projective synchronization in drive-response networks coupled with complex-variable chaotic systems

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Abstract

In drive-response complex-variable systems, projective synchronization with respect to a real number, real matrix, or even real function means that drive-response systems evolve simultaneously along the same or inverse direction in a complex plane. However, in many practical situations, the drive-response systems may evolve in different directions with a constant intersection angle. Therefore, this paper investigates projective synchronization in drive-response networks of coupled complex-variable chaotic systems with respect to complex numbers, called complex projective synchronization (CPS). The adaptive feedback control method is adopted first to achieve CPS in a general drive-response network. For a special class of drive-response networks, the CPS is achieved via pinning control. Furthermore, a universal pinning control scheme is proposed via the adaptive coupling strength method, several simple and useful criteria for CPS are obtained, and all results are illustrated by numerical examples.

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Acknowledgements

This research is jointly supported by the NSFC grant 11072136, Natural Science Foundation of Jiangxi Province of China (20122BAB211006), and Shanghai Leading Academic Discipline Project (S30104).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, 330022, China

    Zhaoyan Wu

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Xinchu Fu

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  1. Zhaoyan Wu
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  2. Xinchu Fu
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Correspondence to Zhaoyan Wu.

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Wu, Z., Fu, X. Complex projective synchronization in drive-response networks coupled with complex-variable chaotic systems. Nonlinear Dyn 72, 9–15 (2013). https://doi.org/10.1007/s11071-012-0685-7

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