Dynamic behaviours for semi-discrete stochastic Cohen-Grossberg neural networks with time delays

Abstract By using semi-discretization technique, a discrete analogue of stochastic Cohen-Grossberg neural networks is formulated. Firstly, the existence of pth mean almost periodic sequence solutions and pth moment global exponential stability of the above semi-discrete stochastic system are investigated with the help of Krasnoselskii’s fixed point theorem and some analysis techniques in stochastic theory. Secondly, the exponential stability and stochastic stabilization for a special discrete stochastic Cohen-Grossberg neural networks are studied. These findings show that stochastic disturbances and small discrete step length have negative effects on the existence of mean almost periodic solutions and moment exponential stability. But they have positive effects on the exponential stability and exponential non-stability for some special models, respectively. Besides, this paper also finds that some unstable neural networks should become exponentially stable by stochastic disturbances. In the end, some examples and computer simulations are given to demonstrate the effectiveness of the theoretical results.

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