Synchronization criteria in complex dynamical networks with nonsymmetric coupling and multiple time-varying delays

Abstract

In this article, we consider a generalized complex dynamical network model with nonsymmetric coupling, and the dynamics of each node has a different time-varying delay. Criteria of exponential synchronization are derived in terms of linear matrix inequalities for the model by constructing suitable Lyapunov functionals. The obtained outcomes are different from those in the current literature, in which the complex dynamical networks are coupling symmetrically and delays are fixed constants. Moreover, the given sufficient conditions extend current available results and are verifiable. A numerical example is provided to illustrate the efficiency of the derived outcome.

Keywords:

• complex dynamical networks
• time-varying delays
• nonsymmetric coupling
• exponential synchronizations

AMS Subject Classifications::

• 34D06
• 37C75

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant Nos 10971240, 10926170 and 10926033, in part by the Natural Science Foundation of Chongqing under Grant Nos CSTC2008BB2364 and CSTC2008BB2366 and in part by the Foundation of Science and Technology project of Chongqing Education Commission under Grant Nos KJ080806 and KJ080805, in part by the NSF 0605181, 1021203 of the US.