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Synchronization in Nearest-neighbor Coupled Oscillators with A Few Shortcuts
Ao Bin,Zheng Zhigang #
Department of Physics, Beijing Normal University
*Correspondence author
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Funding: 教育部博士点基金（No.20060027009）
Opened online:12 February 2010
Accepted by: none
Citation: Ao Bin,Zheng Zhigang.Synchronization in Nearest-neighbor Coupled Oscillators with A Few Shortcuts[OL]. [12 February 2010] http://en.paper.edu.cn/en_releasepaper/content/40188
 
 
Synchronous dynamics in nearest-neighbor coupled chaotic oscillators with a few shortcuts is explored. The existence and stability of the partially synchronous states are studied. It is revealed that different topology of connections among oscillators gives rise to synchronized or unsynchronized dynamics. The criterion for the emergence of the partially synchronized states on a given network is theoretically discussed and proposed. The synchronization for the two-shortcut case are studied in detail, i.e., we prove that partial synchronization is always achievable for parallel networks, while the stability of partial synchronization depends crucially on the topology of connections for crossed and lambda networks. The phase diagram for the transition to partial synchronization is given for different cases. The manifestations for the transition to partial synchronization in relating to the Lyapunov exponent spectra are found and interpreted. These explorations indicate that the microscopic topology of the network have a profound effect on the macroscopic dynamical features of the system.
Keywords:partial synchronization;complex networks;Lyapunov exponents
 
 
 

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