Finite-time synchronization problem of a class of discontinuous Cohen\u2013Grossberg neural networks with mixed delays via new switching design

Zhaohong Xiang,Runjie Li

doi:10.1186/s13662-021-03542-2

Abstract

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.

Highlights

1 Introduction Recently, the research of neural networks with discontinuous activation functions has gradually attracted the attention of many researchers, including systems oscillating under earthquake, power circuits, chaos phenomenon, and dry friction
A large number of results have emerged [10,11,12,13,14,15,16,17] such as the existence, dissipation, and exponential stability of the Cohen–Grossberg neural networks (CGNNs) model
Motivated by the aforementioned works on finite-time synchronization of CGNNs system, this paper aims to realize the finite-time synchronization issue for the considered system CGNNs

Summary

Introduction

The research of neural networks with discontinuous activation functions has gradually attracted the attention of many researchers, including systems oscillating under earthquake, power circuits, chaos phenomenon, and dry friction (see [1,2,3,4]). Abdurahman and his team in [21] studied the exponential lag synchronization for both discrete time-delays and distributed delays CGNNs. It worthy to know that, in 2003, Forti introduced the global stability of a discontinuous right-hand side neural network system via the framework of the theory of Filippov differential inclusions [22, 23]. The literature [26] was the first paper to consider finite-time control of discontinuous chaotic systems, and [27] studied the finite-time synchronization of timedelayed neural networks.

Objectives

Results

Conclusion