Multiple attractors and generalized synchronization in delayed Mackey--Glass systems
Li Dong (李栋), Zheng Zhi-Gang (郑志刚)
Department of Physics and the Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875, China
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.
Received: 06 December 2007
Revised: 02 July 2008
Accepted manuscript online:
Fund: 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.
Cite this article:
Li Dong (李栋), Zheng Zhi-Gang (郑志刚) Multiple attractors and generalized synchronization in delayed Mackey--Glass systems 2008 Chin. Phys. B 17 4009
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