Exponential Stability Of Two Class Of Stochastic Neural Networks With Mixed Delays

This paper is concerned with the existence, uniqueness andexponential stability of equilibrium point of a class of stochastic Hopfieldneural networks with mixed delays, and a class of stochastic reaction-di?usionCohen-Grossberg neural networks with mixed delays, respectively.In Chapter 2, a class of stochastic Hopfield neural networks with mixeddelays is considered. Firstly, employing the method of contraction mappingprinciple and inequality techniques, the su?cient condition to guarantee theexistence, uniqueness of equilibrium point is given. Then, using variationparameter and Razumikhin method, the su?cient conditions to guarantee themean square exponential stability and pth exponential stability of equilibriumpoint are obtained, respectively. The results generalize the earlier publications.In Chapter 3, a class of stochastic reaction-di?usion Cohen-Grossbergneural networks with mixed delays is studied. Using the method of M-matrixtheory, variation parameter and inequality techniques, the su?cient conditionson the existence, uniqueness and the global exponential stability of equilibriumpoint of the networks are obtained.