Neural networks letter: New conditions on synchronization of networks of linearly coupled dynamical systems with non-Lipschitz right-hand sides

Authors:
Bo Liu;Wenlian Lu;Tianping Chen
Affiliations:
Key Laboratory of Nonlinear Mathematics Science, School of Mathematical Sciences, Fudan University, Shanghai 200433, PR China;Centre for Computational Systems Biology, Fudan University, Shanghai, 200433, PR China;Key Laboratory of Nonlinear Mathematics Science, School of Mathematical Sciences, Fudan University, Shanghai 200433, PR China
Venue:
Neural Networks
Year:
2012

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Abstract

In this paper, we study synchronization of networks of linearly coupled dynamical systems. The node dynamics of the network can be very general, which may not satisfy the QUAD condition. We derive sufficient conditions for synchronization, which can be regarded as extensions of previous results. These results can be employed to networks of coupled systems, of which, in particular, the node dynamics have non-Lipschitz or even discontinuous right-hand sides. We also give several corollaries where the synchronization of some specific non-QUAD systems can be deduced. As an application, we propose a scheme to realize synchronization of coupled switching systems via coupling the signals which drive the switchings. Examples with numerical simulations are also provided to illustrate the theoretical results.