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Mean square exponential stability of stochastic delay cellular neural networks

The dynamical behaviors of stochastic neural networks have appeared as a novel subject of research and applications, such as optimization, control, and image processing(see [1-12]). Obviously, finding stability criteria for these neural networks becomes an attractive research problem of importance. Some well results have just appeared, for example, in [1-5], for stochastic delayed Hopfield neural networks and stochastic Cohen-Grossberg neural networks, the linear matrix inequality approach is utilized to establish the sufficient conditions on global stability for the neural networks. In particular, in [2], by using the method of variation parameter and stochastic analysis, the sufficient conditions are given to guarantee the exponential stability of an equilibrium solution. However, there are few results about stochastic effects to the stability property of cellular neural networks with delays in the literature today. In this paper, exponential stability of equilibrium point of stochastic cellular neural networks with delays(SDCNNs) is investigated. Following [13], that activation functions require Lipschitz conditions and boundedness, by utilizing general Lyapunov function, stochastic analysis, Young inequality method and Poincare contraction theory are utilized to derive the conditions guaranteeing the existence of periodic solutions of SDCNNs and the stability of periodic solutions. Different from the LMI (linear matrix inequality) approach [13], [15] and variation parameter method, the Young inequality method is firstly developed to investigate the stability of SDCNN. These sufficient conditions improve and extend the early works in Refs. [18,19], and they include those governing parameters of SDCNNs, so they can be easily checked by simple algebraic methods, comparing with the results of [13-17]. Furthermore, one example is given to demonstrate the usefulness of the results in this paper.