中国物理B ›› 2008, Vol. 17 ›› Issue (11): 4009-4013.doi: 10.1088/1674-1056/17/11/012

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Multiple attractors and generalized synchronization in delayed Mackey--Glass systems

李 栋, 郑志刚   

  1. Department of Physics and the Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875, China
  • 收稿日期:2007-12-06 修回日期:2008-07-02 出版日期:2008-11-20 发布日期:2008-11-20
  • 基金资助:
    Project supported in part by the State Key Program of National Natural Science Foundation of China (Grant No 70431002), the National Basic Research Program of China (Grant No 2007CB814800), and the Doctorate Foundation of the State Education Ministry of China (Grant No 20060027009). Supports from the Research Grant Council (RGC), the Hong Kong Baptist University Faculty Research Grant (FRG), and the Croucher Foundation of Hong Kong are acknowledged.

Multiple attractors and generalized synchronization in delayed Mackey--Glass systems

Li Dong (李栋), Zheng Zhi-Gang (郑志刚)   

  1. Department of Physics and the Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875, China
  • Received:2007-12-06 Revised:2008-07-02 Online:2008-11-20 Published:2008-11-20
  • Supported by:
    Project supported in part by the State Key Program of National Natural Science Foundation of China (Grant No 70431002), the National Basic Research Program of China (Grant No 2007CB814800), and the Doctorate Foundation of the State Education Ministry of China (Grant No 20060027009). Supports from the Research Grant Council (RGC), the Hong Kong Baptist University Faculty Research Grant (FRG), and the Croucher Foundation of Hong Kong are acknowledged.

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摘要： Nonlinear dynamics of the time-delayed Mackey--Glass systems is explored. Coexistent multiple chaotic attractors are found. Attractors with double-scroll structures can be well classified in terms of different return times within one period of the delay time by constructing the Poincar\'{e} section. Synchronizations of the drive--response Mackey--Glass oscillators are investigated. The critical coupling strength for the emergence of generalized synchronization against the delay time exhibits the interesting resonant behaviour. We reveal that stronger resonance effect may be observed when different attractors are applied to the drivers, i.e., more resonance peaks can be found.

关键词: time-delayed Mackey--Glass system, multiple chaotic attractors, return numbers, generalized synchronization

Abstract: Nonlinear dynamics of the time-delayed Mackey--Glass systems is explored. Coexistent multiple chaotic attractors are found. Attractors with double-scroll structures can be well classified in terms of different return times within one period of the delay time by constructing the Poincaré section. Synchronizations of the drive--response Mackey--Glass oscillators are investigated. The critical coupling strength for the emergence of generalized synchronization against the delay time exhibits the interesting resonant behaviour. We reveal that stronger resonance effect may be observed when different attractors are applied to the drivers, i.e., more resonance peaks can be found.

Key words: time-delayed Mackey--Glass system, multiple chaotic attractors, return numbers, generalized synchronization

中图分类号:  (Synchronization; coupled oscillators)

  • 05.45.Xt
05.45.Tp (Time series analysis)