# On the Global Practical Exponential Stability of h-Manifolds for Impulsive Reaction–Diffusion Cohen–Grossberg Neural Networks with Time-Varying Delays

## TL;DR

This paper studies the stability of complex neural networks with delays and impulses, using a new method to ensure practical exponential stability.

## Contribution

A new Lyapunov-type function and less restrictive stability criteria for h-manifolds in impulsive neural networks with time-varying delays.

## Key findings

- Sufficient conditions for global practical exponential stability of h-manifolds are established.
- The proposed method is less restrictive regarding variable domains and diffusion coefficients.
- The results are applied to bidirectional associative memory neural networks with impulsive perturbations.

## Abstract

In this paper, we focus on h-manifolds related to impulsive reaction–diffusion Cohen–Grossberg neural networks with time-varying delays. By constructing a new Lyapunov-type function and a comparison principle, sufficient conditions that guarantee the global practical exponential stability of specific states are established. The states of interest are determined by the so-called h-manifolds, i.e., manifolds defined by a specific function h, which is essential for various applied problems in imposing constraints on their dynamics. The established criteria are less restrictive for the variable domain and diffusion coefficients. The effect of some uncertain parameters on the stability behavior is also considered and a robust practical stability analysis is proposed. In addition, the obtained h-manifolds’ practical stability results are applied to a bidirectional associative memory (BAM) neural network model with impulsive perturbations and time-varying delays. Appropriate examples are discussed.