Pseudo almost periodic solutions for neutral type high-order Hopfield neural networks with mixed time-varying delays and leakage delays on time scales

Abstract

In this paper, a class of neutral type high-order Hopfield neural networks with mixed time-varying delays and leakage delays on time scales is proposed. Based on the exponential dichotomy of linear dynamic equations on time scales, Banach's fixed point theorem and the theory of calculus on time scales, some sufficient conditions are obtained for the existence and global exponential stability of pseudo almost periodic solutions for this class of neural networks. Our results are completely new. Finally, we present an example to illustrate our results are effective. Our example also shows that the continuous-time neural network and its discrete-time analogue have the same dynamical behaviors for the pseudo almost periodicity.

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

“…Lemma Assume and . If 1− ν ( t ) p ( t )>0 for , then for all .…”

“…Definition A time scale is called an almost periodic time scale if …”

“…Recently, the stability of systems with leakage delays has become one of the hot topics . 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.…”

Anti-Periodic Dynamics of Quaternion-Valued Fuzzy Cellular Neural Networks with Time-Varying Delays on Time Scales

“…Fortunately, the time scale theory, which was introduced by Hilger [35], can unify the study of continuous and discrete analysis, and the study of dynamic equations on time scales 2 Discrete Dynamics in Nature and Society can contain, link, and extend the classical theory of differential and difference equations [36]. Recently, the theory of time scale calculus has been applied in real-valued neural networks [37][38][39][40][41][42][43] and complex-valued networks [44]. However, to the best of our knowledge, the existence and global stability of anti-periodic solutions of quaternion-valued fuzzy cellular neural networks (QVFCNNs) on time scales have not been considered yet.…”

“…However, to the best of our knowledge, the existence and global stability of anti-periodic solutions of quaternion-valued fuzzy cellular neural networks (QVFCNNs) on time scales have not been considered yet. Besides, it is well known that time delays are unavoidable in real neural network systems and they may cause the changes of the dynamical behaviors of neural networks [11,25,40,41].…”