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Mean-square exponential stability of stochastic Hopfield neural networks with time-varying discrete and distributed delays. (English) Zbl 1229.92006
Summary: In this Letter, the mean-square exponential stability problem for stochastic Hopfield neural networks with both discrete and distributed time-varying delays is investigated. By choosing a modified Lyapunov-Krasovskii functional, a delay-dependent criterion is established such that the stochastic neural network is mean-square exponentially stable. The derivative of discrete time-varying delay h(t) satisfies h ˙η and the decay rate β can be any finite positive value without any other constraints. The assumptions given in this Letter are more general than the conventional assumptions (i.e., h ˙((t)η<1 and β satisfies a transcendental equation or an inequality). Finally, numerical examples are provided to illustrate the effectiveness of the proposed sufficient conditions.
MSC:
92B20General theory of neural networks (mathematical biology)
68T05Learning and adaptive systems
60K99Special processes
37N25Dynamical systems in biology
34K60Qualitative investigation and simulation of models
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