Pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions
Zou Yan-Li(邹艳丽)a)b)† and Chen Guan-Rong(陈关荣)b)
a College of Physics and Electronic Engineering, Guangxi Normal University, Guilin 541004, China; b Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, China
Abstract This paper studies pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions. To study a state-feedback pinning-controlled network with N nodes, it first converts the controlled network to an extended network of N+1 nodes without controls. It is shown that the controlled synchronizability of the given network is determined by the real part of the smallest nonzero eigenvalue of the coupling matrix of its extended network when the synchronized region is unbounded; but it is determined by the ratio of the real parts of the largest and the smallest nonzero eigenvalues of the coupling matrix when the synchronized region is bounded. Both theoretical analysis and numerical simulation show that the portion of controlled nodes has no critical values when the synchronized region is unbounded, but it has a critical value when the synchronized region is bounded. In the former case, therefore, it is possible to control the network to achieve synchronization by pinning only one node. In the latter case, the network can achieve controlled synchronization only when the portion of controlled nodes is larger than the critical value.
Received: 26 December 2008
Revised: 23 January 2009
Accepted manuscript online:
Fund: Project supported by
the National Natural Science Foundation of China (Grant No
10647001), the Guangxi Natural Science Foundation (Grant No
0728042), the Program for Excellent Talents in Guangxi Higher
Education Institutions (Grant No RC2007006) and the NSFC-HK
Joint Research Scheme (Grant No N-CityU107/07).
Cite this article:
Zou Yan-Li(邹艳丽) and Chen Guan-Rong(陈关荣) Pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions 2009 Chin. Phys. B 18 3337
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