Dynamic behavior of a class of neutral-type neural networks with discontinuous activations and time-varying delays

Abstract

This paper is concerned with a class of neutral-type neural networks with discontinuous activations and time-varying delays. Under the concept of Filippov solution, by applying the differential inclusions and the topological degree theory in set-valued analysis, we employ a novel argument to establish new results on the existence of the periodic solutions for the considered neural networks. After that, we derive some criteria on the uniqueness, global exponential stability of the considered neural networks and convergence of the corresponding autonomous case of the considered neural networks, in terms of nonsmooth analysis theory with Lyapunov-like approach. Without assuming the boundedness (or the growth condition) and monotonicity of the discontinuous neuron activation functions, the results obtained can also be valid. Our results extend previous works on the neutral-type neural networks to the discontinuous cases, some related results in the literature can be enriched and extended. Finally, two typical examples and the corresponding numerical simulations are provided to show the effectiveness and flexibility of the results derived in this paper.