Neural networks with non-smooth and impact activations

TL;DR

This paper studies impulsive recurrent neural networks with non-smooth activations, providing conditions for stability, existence of periodic solutions, and validating results through numerical simulations.

Contribution

It introduces new theoretical results on the existence, uniqueness, and stability of solutions in impulsive neural networks with non-smooth activations.

Findings

Conditions for global asymptotic stability established

Existence of periodic solutions demonstrated

Numerical simulations confirm theoretical results

Abstract

In this paper, we consider a model of impulsive recurrent neural networks with piecewise constant delay. The dynamics are presented by differential equations with discontinuities such as impulses at fixed moments and piecewise constant argument of generalized type. Sufficient conditions ensuring the existence, uniqueness and global asymptotic stability of the equilibrium point are obtained. By employing Green's function we derive new result of existence of the periodic solution. The global asymptotic stability of the solution is investigated. Examples with numerical simulations are given to validate the theoretical results.