Stability Analysis of Cohen–Grossberg Neural Networks with Random Impulses

Ravi Agarwal,Peter Kopanov,Snezhana Hristova,Donal O’Regan

doi:10.3390/math6090144

Abstract

The Cohen and Grossberg neural networks model is studied in the case when the neurons are subject to a certain impulsive state displacement at random exponentially-distributed moments. These types of impulses significantly change the behavior of the solutions from a deterministic one to a stochastic process. We examine the stability of the equilibrium of the model. Some sufficient conditions for the mean-square exponential stability and mean exponential stability of the equilibrium of general neural networks are obtained in the case of the time-varying potential (or voltage) of the cells, with time-dependent amplification functions and behaved functions, as well as time-varying strengths of connectivity between cells and variable external bias or input from outside the network to the units. These sufficient conditions are explicitly expressed in terms of the parameters of the system, and hence, they are easily verifiable. The theory relies on a modification of the direct Lyapunov method. We illustrate our theory on a particular nonlinear neural network.

Highlights

Artificial neural networks are important technical tools for solving a variety of problems in various scientific disciplines
We define the generalization of Cohen and Grossberg neural network with impulses at random times, briefly giving an explanation of the solutions being stochastic processes, and we study stability properties
We study stability properties of the equilibrium point of a generalization of the

Summary

Introduction

Artificial neural networks are important technical tools for solving a variety of problems in various scientific disciplines. Cohen and Grossberg [1] introduced and studied in 1983 a new model of neural networks This model was extensively studied and applied in many different fields such as associative memory, signal processing and optimization problems. Several authors generalized this model [2] by including delays [3,4], impulses at fixed points [5,6] and discontinuous activation functions [7]. We define the generalization of Cohen and Grossberg neural network with impulses at random times, briefly giving an explanation of the solutions being stochastic processes, and we study stability properties. Some stability sufficient criteria are provided and illustrated with examples

System Description

Stability Analysis of Neural Networks with Random Impulses

Conclusions