Periodic Solutions for Impulsive Stochastic BAM Neural Networks with Time-Varying Delays in Leakage Terms

By using an integral inequality, we establish some sufficient conditions for the existence and p-exponential stability of periodic solutions for a class of impulsive stochastic BAM neural networks with time-varying delays in leakage terms. Moreover, we present an example to illustrate the feasibility of our results. 1. Introduction Since it was proposed by Kosko (see [1]), the bidirectional associative memory (BAM) neural networks have attracted considerable attentions due to their extensive applications in classification of patterns, associative memories, image processing, and other areas. In the past few years, many scholars have obtained lots of good results on the dynamical behaviors analysis of BAM neural networks. The reader may see [2–8] and the references therein. But in a real nervous system, it is usually unavoidably affected by external perturbations which are in many cases of great uncertainty and hence may be treated as random. As pointed out by Haykin [9], in real nervous systems, synaptic transmission is a noisy process brought on by random fluctuations from the release of neurotransmitters and other probabilistic causes. And the stability of neural networks could be stabilized or destabilized by some stochastic inputs [10]. Therefore, it is significant and of prime importance to consider the dynamics of stochastic neural networks. With respect to stochastic neural networks, there are many works on the stability. For example, in？？[11–17], the scholars studied the stability of different classes of stochastic neural networks. For other results on stochastic neural networks, the reader may see？？[18–23] and the references therein. However, the above results are mainly on the stability of considered stochastic neural networks. And it is well known that studies on neural dynamical systems not only involve a discussion of stability properties, but also involve many dynamic behaviors such as periodic oscillatory behavior. On the other hand, the neural networks are often subject to impulsive effects that in turn affect dynamical behaviors of the systems. Moreover, a leakage delay, which is the time delay in the leakage term of the systems and a considerable factor affecting dynamics for the worse in the systems, is being put to use in the problem of stability for neural networks. However, so far, very little attention has been paid to neural networks with time delay in the leakage (or “forgetting”) term. Such time delays in the leakage term are difficult to handle but have great impact on the dynamical behavior of neural networks. Therefore, it is