Almost automorphic solution for neutral type high-order Hopfield BAM neural networks with time-varying leakage delays on time scales

Abstract

In this paper, by applying the exponential dichotomy theory on time scales, Banach contraction mapping principle and differential inequality analysis techniques, we establish some sufficient conditions for the existence and global exponential stability of almost automorphic solution for neutral type high-order Hopfield bidirectional associative memory (BAM) neural networks with time-varying leakage delays on time scales. In the addressed system, we not only consider the effects of the first-order neutral terms on networks, but also investigate the influences of the second-order neutral terms on the networks. High-order Hopfield BAM neural networks with continuously distributed leakage delays on time scales are also considered. Our results are completely new even if time scale T=R or T=Z and complementary to the previously existing results. Finally, three examples with numerical simulations are presented to illustrate the feasibility of our proposed theoretical results.