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A new method to realize cluster synchronization in connected chaotic networks.

Zhongjun Ma1, Zengrong Liu, Gang Zhang

  • 1College of Sciences, Shanghai University, Shanghai, 200444, China. mzj234402@163.com

Chaos (Woodbury, N.Y.)
|July 11, 2006
PubMed
Summary

This study introduces a new coupling method to achieve stable cluster synchronization patterns in chaotic networks. The cooperative and competitive weight-couplings ensure global stability for selected synchronization patterns.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Network Science

Background:

  • Chaotic networks exhibit complex behaviors and synchronization phenomena.
  • Controlling synchronization patterns in chaotic systems is crucial for various applications.
  • Existing methods may have limitations in achieving arbitrarily selected cluster synchronization.

Purpose of the Study:

  • To develop a novel method for stabilizing arbitrarily selected cluster synchronization patterns in connected chaotic networks.
  • To derive a sufficient condition for the global stability of these synchronization patterns.
  • To demonstrate the effectiveness of the proposed method through a practical example.

Main Methods:

  • A new coupling scheme is proposed, utilizing cooperative and competitive weight-couplings.

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  • The method constructs a specific coupling strategy tailored to the desired synchronization pattern.
  • Mathematical analysis is employed to derive conditions for global stability.

    • Main Results:

    • The proposed coupling scheme successfully stabilizes arbitrarily selected cluster synchronization patterns.
    • A sufficient condition for the global stability of these patterns is derived.
    • The method is shown to be effective in connected chaotic networks.

    Conclusions:

    • The novel coupling scheme provides a robust method for achieving desired cluster synchronization in chaotic networks.
    • The derived stability condition offers a theoretical guarantee for pattern stabilization.
    • This work contributes to the control and understanding of synchronization in complex dynamical systems.