On the Stability with Respect to H-Manifolds for Cohen–Grossberg-Type Bidirectional Associative Memory Neural Networks with Variable Impulsive Perturbations and Time-Varying Delays

Gani Stamov,Ivanka Stamova,Ivan Torlakov,Stanislav Simeonov

doi:10.3390/math8030335

Abstract

The present paper is devoted to Bidirectional Associative Memory (BAM) Cohen–Grossberg-type impulsive neural networks with time-varying delays. Instead of impulsive discontinuities at fixed moments of time, we consider variable impulsive perturbations. The stability with respect to manifolds notion is introduced for the neural network model under consideration. By means of the Lyapunov function method sufficient conditions that guarantee the stability properties of solutions are established. Two examples are presented to show the validity of the proposed stability criteria.

Highlights

The Cohen–Grossberg-type neural network models were first proposed by Cohen and Grossberg [1] in 1983, and since an extensive work on this subject has been done by numerous researchers due to the opportunities for applications of such models in key fields of science and engineering such as parallel computing, associative memory, pattern recognition, signal and image processing, etc. [2,3,4]
It is well known that Bidirectional Associative Memory (BAM) neural networks were first proposed by Kosko [5,6,7]
It is well known that time delays naturally exist in neural network models, due mainly to the limited speed of signal transmissions and amplifiers switching

Summary

Introduction

The Cohen–Grossberg-type neural network models were first proposed by Cohen and Grossberg [1] in 1983, and since an extensive work on this subject has been done by numerous researchers due to the opportunities for applications of such models in key fields of science and engineering such as parallel computing, associative memory, pattern recognition, signal and image processing, etc. [2,3,4]. In [39] the problem of existence of equilibrium states of Cohen–Grossberg BAM neural networks with delays and impulses and their global exponential stability behavior are investigated using topological degree theory, the Lyapunov functional method and some analysis techniques. Stimulated by the above discussions, in this paper, we will generalize the concept of the stability of a single solution, and investigate the stability of Cohen–Grossberg-type BAM impulsive neural networks with time-varying delays and variable impulsive perturbations with respect to manifolds. These manifolds will be determined by particular functions [55].

Preliminary Notes

The functions Pik and Q jk are such that

Illustrative Examples

Conclusions