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Finite-time synchronization of complex networks with nonidentical discontinuous nodes. (English) Zbl 1281.34100
Summary: In this paper, we study the finite-time synchronization problem for linearly coupled complex networks with discontinuous nonidentical nodes. Firstly, new conditions for general discontinuous chaotic systems is proposed, which is easy to be verified. Secondly, a set of new controllers are designed such that the considered model can be finite-timely synchronized onto any target node with discontinuous functions. Based on a finite-time stability theorem for equations with discontinuous right-hand and inequality techniques, several sufficient conditions are obtained to ensure the synchronization goal. Results of this paper are general, and they extend and improve existing results on both continuous and discontinuous complex networks. Finally, numerical example, in which a BA scale-free network with discontinuous Sprott and Chua circuits is finite-timely synchronized onto discontinuous Chen system, is given to show the effectiveness of our new results.

MSC:
34D06 Synchronization of solutions to ordinary differential equations
05C82 Small world graphs, complex networks (graph-theoretic aspects)
34C28 Complex behavior and chaotic systems of ordinary differential equations
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