中国物理B ›› 2007, Vol. 16 ›› Issue (6): 1597-1602.doi: 10.1088/1009-1963/16/6/018

• GENERAL • 上一篇    下一篇

Complete synchronization between two bi-directionally coupled chaotic systems via an adaptive feedback controller

肖玉柱, 徐伟   

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China
  • 修回日期:2006-12-20 出版日期:2007-06-20 发布日期:2007-06-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10472091, 10502042 and 10332030) and Graduate Starting Seed Fund of Northwestern Polytechnical University (Grant No Z200655).

Complete synchronization between two bi-directionally coupled chaotic systems via an adaptive feedback controller

Xiao Yu-Zhu(肖玉柱)† and Xu Wei(徐伟)   

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China
  • Revised:2006-12-20 Online:2007-06-20 Published:2007-06-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10472091, 10502042 and 10332030) and Graduate Starting Seed Fund of Northwestern Polytechnical University (Grant No Z200655).

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摘要： In this paper, we apply a simple adaptive feedback control scheme to synchronize two bi-directionally coupled chaotic systems. Based on the invariance principle of differential equations, sufficient conditions for the global asymptotic synchronization between two bi-directionally coupled chaotic systems via an adaptive feedback controller are given. Unlike other control schemes for bi-directionally coupled systems, this scheme is very simple to implement in practice and need not consider coupling terms. As examples, the autonomous hyperchaotic Chen systems and the new non-autonomous 4D systems are illustrated. Numerical simulations show that the proposed method is effective and robust against the effect of weak noise.

Abstract: In this paper, we apply a simple adaptive feedback control scheme to synchronize two bi-directionally coupled chaotic systems. Based on the invariance principle of differential equations, sufficient conditions for the global asymptotic synchronization between two bi-directionally coupled chaotic systems via an adaptive feedback controller are given. Unlike other control schemes for bi-directionally coupled systems, this scheme is very simple to implement in practice and need not consider coupling terms. As examples, the autonomous hyperchaotic Chen systems and the new non-autonomous 4D systems are illustrated. Numerical simulations show that the proposed method is effective and robust against the effect of weak noise.

Key words: complete synchronization, bi-directionally coupled systems, adaptive control

中图分类号:  (Control of chaos, applications of chaos)

  • 05.45.Gg
05.45.Xt (Synchronization; coupled oscillators)