Finite-time synchronization of coupled discontinuous neural networks with mixed delays and nonidentical perturbations

Abstract This paper is concerned with the finite-time synchronization in an array of coupled neural networks with discontinuous activation functions, discrete and unbounded distributed delays (mixed delays), and norm-bounded nonidentical perturbations. Under the framework of Filippov solution, we first derive some general sufficient conditions to guarantee the global existence of the solutions to the neural networks with discontinuous activation functions and mixed delays. Then, by designing simple controller, applying some new analytical techniques, and constructing some new Lyapunov–Krasovskii functionals, several sufficient conditions are derived to ensure the finite-time synchronization of the considered networks. Moreover, the setting time is also estimated for the network under study with bounded delays or without delays. In sharp contrast to the existed results which can only finite-timely synchronize or stabilize the non-delayed systems, the theoretical results of this paper are more general and rigorous. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

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