Stability Results for Uncertain Stochastic High-Order Hopfield Neural Networks with Time Varying Delays

Abstract

Neural networks have been widely applied in image processing, pattern recognition, optimization solvers, fixed-point computation and other engineering areas. It has been known that these applications heavily depend on the dynamic behaviors of neural networks. The stability of neural networks has been extensively studied over the past years because it is one of the most important behaviors of neural networks. On the other hand, time delays are frequently encountered in neural networks due to the finite switching speed of amplifiers and the inherent communication time of neurons. Since the existence of time delay is often a source of instability for neural networks, the stability study for delayed neural networks is of both theoretical and practical importance. Hopfield [9, 10] has proposed Hopfield neural networks (HNNs) which have found applications in a broad range of disciplines where the targeted problems can reduce to optimization problems. In recent years, HNNs and their various generalizations have attracted the great attention of many scientists including mathematicians, physicists, computer scientists due to their potential for the tasks of classification, associative memory, parallel computation and their ability to solve difficult optimization problems, see for example [4, 10, 13]. HNNs characterized by first-order interactions, [1, 14] presented their intrinsic limitations. Recently, the study of high-order neural networks has received much attention due to that they have stronger approximation property, faster convergence rate, greater storage capacity and higher fault tolerance than lower-order neural networks [17]. In [3, 5, 6, 8, 11, 12, 15, 16, 18, 19, 22], the authors have been studied the stability analysis of high-order neural networks with constant time delays or time varying delays. In this paper, we are concerned with the global stability for a class of uncertain stochastic high-order neural networks with time varying delays. The structure of the stochastic neural networks under consideration is more general than some previous ones existed in the literature. Based on the Lyapunov stability theory, new global asymptotic stability criteria are presented in