Periodicity and global exponential periodic synchronization of delayed neural networks with discontinuous activations and impulsive perturbations

In this paper, periodic dynamics and periodic synchronization of a class of delayed neural networks with discontinuous neuron activations and impulsive perturbations are investigated. Firstly, based on Filippov's functional differential inclusion and impulsive differential inclusions theory, the existence of solutions of the considered neural network system is studied. Secondly, according to Krasnoselskii's fixed point theorem on cones of set-valued analysis, sufficient conditions are provided for the existence of at least one periodic solution and at least two periodic solutions for the neural network systems. Furthermore, we also use Kakutani's fixed point theorem to give sufficient criteria for the existence of at least one periodic solution of the neural network systems. These results shown that there are still one or more periodic solutions for the neural networks with discontinuous activations under the impulsive effects. Moreover, sufficient criteria are given to the exponential periodic synchronization under the switching state-feedback control strategy with or without delay. Finally, two numerical simulation examples are presented to verify the correctness and validity of our main conclusions. (C) 2020 Elsevier B.V. All rights reserved.