Generalized non-autonomous Cohen-Grossberg neural network model

TL;DR

This paper establishes new stability and periodic solution criteria for a generalized Cohen-Grossberg neural network with unbounded delays, using the dominate of non-delay terms and the coincide degree theorem.

Contribution

It introduces novel stability and periodic solution conditions for a broad class of neural networks with complex delay structures, extending existing theoretical frameworks.

Findings

Derived stability criteria based on non-delay term dominance

Established existence of periodic solutions using the coincide degree theorem

Validated results with numerical simulations

Abstract

In the present paper, we investigate both the global exponential stability and the existence of a periodic solution of a general differential equation with unbounded distributed delays. The main stability criterion depends on the dominance of the non-delay terms over the delay terms. The criterion for the existence of a periodic solution is obtained with the application of the coincide degree theorem. We use the main results to get criteria for the existence and global exponential stability of periodic solutions of a generalized higher-order periodic Cohen-Grossberg neural network model with discrete-time varying delays and infinite distributed delays. Additionally, we provide a comparison with the results in the literature and a numerical simulation to illustrate the effectiveness of some of our results.