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Motivated by the fact that the multi-stable property is becoming more and more important both in biological neural networks and in artificial intelligence, this paper is concerned with the multi-synchronization problem of stochastic coupled multi-stable-state neural networks (SCMNNs) with time-varying delay. First, we give the sufficient conditions to guarantee that every sub-system or sub-network owns more than one stable points or locally exponential stable periodic orbits. Second, via the impulsive control strategy and by choosing an appropriate Lyapunov function, some sufficient conditions for multi-synchronization of the controlled time-varying delayed SCMNNs are achieved. Moreover, by use of obtained sufficient conditions, which are expressed in the form of linear matrix inequalities, a novel control protocol based on the impulsive system theory for time-varying delayed SCMNNs with two types of topological structure is devised. The validity of the proposed results is verified by a numerical simulation.

Multi-Synchronization of Stochastic Coupled Multi-Stable Neural Networks With Time-Varying Delay by Impulsive Control