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Existence and global asymptotic stability of periodic solutions for Hopfield neural networks with discontinuous activations. (English) Zbl 1160.92002
Summary: We study a class of neural networks with discontinuous activations, which include bidirectional associative memory networks and cellular networks as its special cases. By the Leray-Schauder alternative theorem, matrix theory and a generalized Lyapunov approach, we obtain some sufficient conditions ensuring the existence, uniqueness and global asymptotic stability of periodic solutions. Our results are less restrictive than previously known criteria and can be applied to neural networks with a broad range of activation functions assuming neither boundedness nor monotonicity.
MSC:
92B20General theory of neural networks (mathematical biology)
68T05Learning and adaptive systems
34C25Periodic solutions of ODE
34D23Global stability of ODE