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Synchronization rate of synchronized coupled systems

Author

Listed:
  • Xiong, Xiaohua
  • Hong, Shangnan
  • Wang, Junwei
  • Gan, Dengwen

Abstract

Synchronization phenomena, an emergent property in networks of interacting dynamical elements, are widely observed in nature, and have become the subject of intense research. Here we will investigate the synchronization rate problem in coupled limit-cycle and chaotic oscillators. Based on the mode decomposition method and Gershgörin's discs theorem, some sufficient conditions for synchronization of coupled systems are obtained, and a synchronization rate is then derived. Such a synchronization rate indicates that the error functions between state variables of underlying individual systems tend to zero in the exponential form as time tends to the infinity. Several numerical examples are also given to validate the theoretical results.

Suggested Citation

  • Xiong, Xiaohua & Hong, Shangnan & Wang, Junwei & Gan, Dengwen, 2007. "Synchronization rate of synchronized coupled systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 689-699.
    • Handle: RePEc:eee:phsmap:v:385:y:2007:i:2:p:689-699
    DOI: 10.1016/j.physa.2007.07.003
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    References listed on IDEAS

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    1. Wang, Junwei & Zhou, Tianshou, 2007. "Chaos synchronization based on contraction principle," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 163-170.
    2. Wang, Junwei & Xiong, Xiaohua & Zhang, Yanbin, 2006. "Extending synchronization scheme to chaotic fractional-order Chen systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 279-285.
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    Cited by:

    1. Mitul Islam & Bipul Islam & Nurul Islam, 2013. "Rate Estimation of Identical Synchronization by Designing Controllers," Journal of Mathematics, Hindawi, vol. 2013, pages 1-8, May.

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