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Complex projective synchronization in coupled chaotic complex dynamical systems

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Abstract

In previous papers, the projective factors are always chosen as real numbers, real matrices, or even real-valued functions, which means the coupled systems evolve in the same or inverse direction simultaneously. However, in many practical situations, the drive-response systems may evolve in different directions with a constant intersection angle. Therefore, the projective synchronization with respect to a complex factor, called complex projective synchronization (CPS), should be taken into consideration. In this paper, based on Lyapunov stability theory, three typical chaotic complex dynamical systems are considered and the corresponding controllers are designed to achieve the complex projective synchronization. Further, an adaptive control method is adopted to design a universal controller for partially linear systems. Numerical examples are provided to show the effectiveness of the proposed method.

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Authors and Affiliations

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

    Zhaoyan Wu

  2. Institute for Pure and Applied Mathematics, University of California, Los Angeles, CA, 90095-7121, USA

    Jinqiao Duan

  3. Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL, 60616, USA

    Jinqiao Duan

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

    Xinchu Fu

Authors
  1. Zhaoyan Wu
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  2. Jinqiao Duan
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  3. Xinchu Fu
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Correspondence to Xinchu Fu.

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Wu, Z., Duan, J. & Fu, X. Complex projective synchronization in coupled chaotic complex dynamical systems. Nonlinear Dyn 69, 771–779 (2012). https://doi.org/10.1007/s11071-011-0303-0

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  • DOI: https://doi.org/10.1007/s11071-011-0303-0

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