Exponential Synchronization of the Linearly Coupled Dynamical Networks with Delays*

Abstract

In this paper, the authors investigate the synchronization of an array of linearly coupled identical dynamical systems with a delayed coupling. Here the coupling matrix can be asymmetric and reducible. Some criteria ensuring delay-independent and delay-dependent global synchronization are derived respectively. It is shown that if the coupling delay is less than a positive threshold, then the coupled network will be synchronized. On the other hand, with the increase of coupling delay, the synchronization stability of the network will be restrained, even eventually de-synchronized.

Keywords

Time-delay / Synchronization / Exponential stability / Left eigenvector / 17B40 / 17B50

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