Existence and exponential stability of almost periodic solutions for neutral‐type BAM neural networks with distributed leakage delays

Abstract

This paper is concerned with a class of neutral‐type BAM neural networks with distributed leakage delays. By applying the exponential dichotomy of linear differential equations, Lyapunov functional method and contraction mapping principle, we establish some sufficient conditions which ensure the existence and exponential stability of almost periodic solutions for such BAM neural networks. An example is given to illustrate the effectiveness of the theoretical findings. The results obtained in this article are completely new and complement the previously known studies. 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

“…A typical time delay called as leakage delay may exist in the negative feedback terms of the system, and it has a great impact on the dynamic behaviors of the neural networks, such as on the instability or poor system performance of neural networks. On the basis of the aforementioned arguments, the study of delayed BAM neural networks in the leakage term and its analogous equations has attracted worldwide interest . In fact, it is natural and important that systems contain some information about the derivative of the past state to further describe and model the dynamics for such complex neural reactions.…”

“…On the basis of the aforementioned arguments, the study of delayed BAM neural networks in the leakage term and its analogous equations has attracted worldwide interest. 26,32,33 In fact, it is natural and important that systems contain some information about the derivative of the past state to further describe and model the dynamics for such complex neural reactions. Many researchers have studied the dynamics of various classes of neutral-type neural networks.…”

“…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.…”

Novel Criteria of ISS Analysis for Delayed Memristive Simplified Cohen–Grossberg BAM Neural Networks

“…ere have been many results on the stability for BAM neural networks with or without delays [2][3][4][5][6][7][8]. At the same time, in 1983, Cohen and Grossberg discussed a class of competitive neural networks, which is called Cohen-Grossberg neural networks.…”

Existence, uniqueness and global asymptotic stability for a class of complex-valued neutral-type neural networks with time delays

“…Two types of time delays are generally considered in nonlinear system in the literature, i. e., the retarded-type delays and neutral-type delays [15,44]. Retarded-type NNs that have only time-delays in the states are not good enough to characterize precisely the complicated dynamic properties of the neural cells in real world, so neutral-type NNs that involve time delays in the time derivatives of states have attracted much attention [5,8,18,20,21,22,23,36,39,41,42].…”