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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:

92B20 Neural networks for/in biological studies, artificial life and related topics
68T05 Learning and adaptive systems in artificial intelligence
34C25 Periodic solutions to ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
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