Existence and Global Logarithmic Stability of Impulsive Neural Networks with Time Delay

TL;DR

This paper investigates the existence and global logarithmic stability of impulsive neural networks with time delay, using Lyapunov functions to analyze stability in systems with inherent delays.

Contribution

It introduces a method to establish logarithmic stability for impulsive delayed neural networks through Lyapunov function construction.

Findings

Proves the existence of stable solutions under certain conditions

Provides criteria for global logarithmic stability

Extends stability analysis to impulsive neural networks with delays

Abstract

The stability and convergence of the neural networks are the fundamental characteristics in the Hopfield type networks. Since time delay is ubiquitous in most physical and biological systems, more attention is being made for the delayed neural networks. The inclusion of time delay into a neural model is natural due to the finite transmission time of the interactions. The stability analysis of the neural networks depends on the Lyapunov function and hence it must be constructed for the given system. In this paper we have made an attempt to establish the logarithmic stability of the impulsive delayed neural networks by constructing suitable Lyapunov function.