Finite-time synchronization problem of a class of discontinuous Cohen–Grossberg neural networks with mixed delays via new switching design

This paper investigates a class of generalized Cohen–Grossberg neural networks (CGNNs) with discontinuous activations and mixed delays. Based on the nonsmooth analysis theory, the drive-response concept, differential inclusions theory, we give several basic assumptions to gain the finite-time synchronization issue of CGNNs. Sufficient conditions are provided without the boundedness or monotonicity of discontinuous activation functions. Moreover, one can estimate the settling time’s upper bounds of the system. At last, two numerical examples and their simulations are given to further show the benefits of the obtained control approach.

Global exponential stability of periodic solution of delayed discontinuous Cohen–Grossberg neural networks and its applications

This paper is concerned with the existence and global exponential stability of the periodic solution of delayed Cohen–Grossberg neural networks (CGNNs) with discontinuous activation functions. The activations considered herein are non-decreasing but not required to be Lipschitz or continuous. Based on differential inclusion theory, Lyapunov functional theory and Leary–Schauder alternative theorem, some sufficient criteria are derived to ensure the existence and global exponential stability of the periodic solution. In order to show the superiority of the obtained results, an application and some detailed comparisons between some existing related results and our results are presented. Finally, some numerical examples are also illustrated.

Robust Fixed-Time Synchronization for Coupled Delayed Neural Networks with Discontinuous Activations Subject to a Quadratic Polynomial Growth

In this paper, we focus on the robust fixed-time synchronization for discontinuous neural networks (NNs) with delays and hybrid couplings under uncertain disturbances, where the growth of discontinuous activation functions is governed by a quadratic polynomial. New state-feedback controllers, which include integral terms and discontinuous factors, are designed. By Lyapunov–Krasovskii functional method and inequality analysis technique, some sufficient criteria, which ensue that networks can realize the robust fixed-time synchronization, are addressed in terms of linear matrix inequalities (LMIs). Moreover, the upper bound of the settling time, which is independent on the initial values, can be determined to any desired values in advance by the configuration of parameters in the proposed control law. Finally, two examples are provided to illustrate the validity of the theoretical results.

Adaptive synchronization for fractional stochastic neural network with delay

Under the Brownian motion environment, adaptive synchronization is mainly studied in this paper for fractional-order stochastic neural networks (FSNNs) with time delays and discontinuous activation functions. Firstly, an existence theorem of solutions is established and global solutions of FNNs are obtained under the definition of Filippov solution by using the fixed-point theorem for a condensing map. Secondly, an adaptive controller is designed to ensure the synchronization between FNNs and the corresponding fractional-order FSNNs. Finally, a numerical example is given to illustrate the given results.