中国物理B ›› 2005, Vol. 14 ›› Issue (8): 1517-1521.doi: 10.1088/1009-1963/14/8/007

• GENERAL • 上一篇    下一篇

Chaotic dynamics and synchronization of fractional-order Genesio--Tesi systems

卢俊国   

  1. Department of Automation, Shanghai Jiaotong University,Shanghai 200030, China
  • 出版日期:2005-07-13 发布日期:2005-07-13
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 60404005).

Chaotic dynamics and synchronization of fractional-order Genesio--Tesi systems

Lu Jun-Guo (卢俊国)   

  1. Department of Automation, Shanghai Jiaotong University,Shanghai 200030, China
  • Online:2005-07-13 Published:2005-07-13
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 60404005).

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摘要： In this paper, we investigate numerically the chaotic behaviours in the fractional-order Genesio--Tesi system. We find that chaos exists in the fractional-order Genesio--Tesi system with order less than 3. The lowest order we find to have chaos is 2.4 in this fractional-order Genesio--Tesi system. We propose a drive-response synchronization method for synchronizing the fractional-order chaotic Genesio--Tesi systems only using a scalar drive signal. This synchronization approach, based on stability theory of fractional-order systems, is simple and theoretically rigorous. It does not require the computation of the conditional Lyapunov exponents.Simulation results are used to visualize and illustrate the effectiveness of the proposed synchronization method.

Abstract: In this paper, we investigate numerically the chaotic behaviours in the fractional-order Genesio--Tesi system. We find that chaos exists in the fractional-order Genesio--Tesi system with order less than 3. The lowest order we find to have chaos is 2.4 in this fractional-order Genesio--Tesi system. We propose a drive-response synchronization method for synchronizing the fractional-order chaotic Genesio--Tesi systems only using a scalar drive signal. This synchronization approach, based on stability theory of fractional-order systems, is simple and theoretically rigorous. It does not require the computation of the conditional Lyapunov exponents.Simulation results are used to visualize and illustrate the effectiveness of the proposed synchronization method.

Key words: chaos, synchronization, Genesio--Tesi system, fractional-order system, fractional calculus

中图分类号:  (Synchronization; coupled oscillators)

  • 05.45.Xt
02.60.-x (Numerical approximation and analysis)