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Multi-almost periodicity in semi-discretizations of a general class of neural networks. (English) Zbl 07312603

Summary: In this paper, we present multi-almost periodicity of a general class of discrete-time neural networks derived from a well-known semi-discretization technique, that is, coexistence and exponential stability of \(2^N\) almost periodic sequence solutions of discrete-time neural networks subjected to external almost periodic stimuli. By using monotonicity and boundedness of activation functions, we construct \(2^N\) close regions to attain the existence of almost periodic sequence solutions. Meanwhile, some new and simple criteria are derived for the networks to converge exponentially toward \(2^N\) almost periodic sequence solutions. As special cases, our results can extend to discrete-time analogues of periodic or autonomous neural networks and hence complement or improve corresponding existing ones. Finally, computer numerical simulations are performed to illustrate multi-almost periodicity of semi-discretizations of neural networks.

MSC:

39-XX Difference and functional equations
92-XX Biology and other natural sciences
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