Periodicity and multi-periodicity generated by impulses control in delayed Cohen–Grossberg-type neural networks with discontinuous activations

Abstract

This paper discusses the periodicity and multi-periodicity in delayed Cohen–Grossberg-type neural networks (CGNNs) possessing impulsive effects, whose activation functions possess discontinuities and are allowed to be unbounded or nonmonotonic. Based on differential inclusion and cone expansion–compression fixed-point theory of set-valued mapping, several improved criteria are given to derive the positive solution with ω-periodicity and ω-multi-periodicity for delayed CGNNs under impulsive control. These ω-periodicity/ω-multi-periodicity orbits are produced by impulses control. The analytical method and theoretical results presented in this paper are of certain significance to the design of neural network models or circuits possessing discontinuous neuron activation and impulsive effects in periodic environment.