Adaptive synchronization under almost every initial data for stochastic neural networks with time-varying delays and distributed delays. (English) Zbl 1221.93247

Zhu, Quanxin; Cao, Jinde

Commun. Nonlinear Sci. Numer. Simul. 16, No. 4, 2139-2159 (2011).

Summary: This paper is concerned with the adaptive synchronization problem for a class of stochastic delayed neural networks. Based on the LaSalle invariant principle of stochastic differential delay equations and the stochastic analysis theory as well as the adaptive feedback control technique, a linear matrix inequality approach is developed to derive some novel sufficient conditions achieving complete synchronization of unidirectionally coupled stochastic delayed neural networks. In particular, the synchronization criterion considered in this paper is the globally almost surely asymptotic stability of the error dynamical system, which has seldom been applied to investigate the synchronization problem. Moreover, the delays proposed in this paper are time-varying delays and distributed delays, which have rarely been used to study the synchronization problem for coupled stochastic delayed neural networks. Therefore, the results obtained in this paper are more general and useful than those given in the previous literature. Finally, two numerical examples and their simulations are provided to demonstrate the effectiveness of the theoretical results.

MSC:

93D21	Adaptive or robust stabilization
34K50	Stochastic functional-differential equations
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
92B20	Neural networks for/in biological studies, artificial life and related topics

Keywords:

adaptive synchronization; time-varying delay; distributed delay; stochastic neural network; linear matrix inequality; Lasalle invariant principle; adaptive feedback control

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