Global exponential stability for interval general bidirectional associative memory (BAM) neural networks with proportional delays

Abstract

This paper is concerned with interval general bidirectional associative memory (BAM) neural networks with proportional delays. Using appropriate nonlinear variable transformations, the interval general BAM neural networks with proportional delays can be equivalently transformed into the interval general BAM neural networks with constant delays. The sufficient condition for the existence and uniqueness of equilibrium point of the model is established by applying Brouwer's fixed point theorem. By constructing suitable delay differential inequalities, some sufficient conditions for the global exponential stability of the model are obtained. Two examples are given to illustrate the effectiveness of the obtained results. This paper ends with a brief conclusion. Copyright © 2016 John Wiley & Sons, Ltd.

Dynamics of BAM neural networks with mixed delays and leakage time‐varying delays in the weighted pseudo–almost periodic on time‐space scales

“…In one study, the authors establish some results about the existence and the global exponential stability of weighted pseudo–almost periodic solutions to linear dynamic equations on time scales and apply the results for a class of cellular neural networks with discrete delays on time scales. By Brouwer's fixed‐point theorem, a series of new sufficient conditions to guarantee the existence and uniqueness of equilibrium point of the interval general BAM neural networks with proportional delays are established, and the global exponential stability of the neural networks is derived by constructing suitable delay differential inequalities in Xu et al Xu et al establish some sufficient conditions that ensure the existence and the exponential stability of almost periodic solutions for BAM neural networks with distributed leakage delays by applying the exponential dichotomy of linear differential equations, Lyapunov functional method, and contraction mapping principle.…”

Finite Time Synchronization for Stochastic Fractional-Order Memristive BAM Neural Networks with Multiple Delays

“…The focus of their investigation was on analyzing the global exponential stability of the equilibrium point and studying its characteristics in this model. The time delay BAMNNs has been advanced by its positive impact on its development [10][11][12][13].…”

Finite-Time Synchronization for Stochastic Fractional-Order Memristive BAM Neural Networks with Multiple Delays

“…The focus of their investigation was on analyzing the global exponential stability of the equilibrium point and studying its characteristics in this model. The time-delay BAMNNs have been advanced by its positive impact on their development [15][16][17][18].…”