dynamicalnetworks.PDF

Available online at Physica A 334 (2004) 281–302 /locate/physa Chaos synchronization o fgeneral complex dynamical networks Jinhu Lua;b , Xinghuo Yub ;∗, Guanrong Chenc a Institute of Systems Science, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China b School of Electrical and Computer Engineering, RMI TUniversity, GPO Box 2476V, Melbourne, VIC. 3001, Australia cDepartment of Electronic Engineering, City University of Hong Kong, China Received 20 August 2003 Abstract Recently, it has been demonstrated that many large-scale complex dynamical networks display a collective synchronization motion. Here, we introduce a time-varying complex dynamical net- work model and further investigate its synchronization phenomenon. Based on this new complex network model, two network chaos synchronization theorems are proved. We show that the chaos synchronization o fa time-varying complex network is determined by means o fthe inner coupled link matrix, the eigenvalues and the corresponding eigenvectors o fthe coupled conguration ma- trix, rather than the conventional eigenvalues o fthe coupled conguration matrix for a uniform network. Especially, we do not assume that the coupled conguration matrix is symmetric and its o-diagonal elements are nonnegative, which in a way generalizes the related results existing in the literature. c 2003 Elsevier B.V. All rights reserved. PACS: 84.35.+i; 05.45.+b Keywords: Com