An Analysis On The Stability Of Hopfield Neural Networks With Mixed Delay

Stochastic differential equations are an important tool for researching the stochastic dynamic systems.The time delay is an important feature of the dynamic systems.Stochastic Differential systems with discrete or distributed delays have been considered a lot and received many important results.However,in the real world,we often need to consider both of the two delays,which is so-called mixed delay stochastic differential models.So the mixed delays are increasingly important in today's research.This paper considers a stochastic neural network system with mixed delays.Neural network models have been applied successfully in many fields,such as pattern recognition and image processing,which highly require stabilities.We know that random disturbances and delays are not able to avoid when transmit informations between neurons.They will influence the stability of the system directly.Therefore,stability is the core of the research in neural network.Currently,most of the research considered the exponential stability with discrete or distributed time delays.This paper discusses the stability of stochastic Hopfield neural networks with mixed delays on this basis.It mainly includes the following aspects:First,we discuss the mean square exponential stability of the stochastic Hopfield neural networks with mixed delays.Second,we discuss the p-moment stability and almost everywhere stability.Meanwhile,the p-moment exponential stability and almost everywhere exponential stability are its special cases,then we extend the result to the stochastic Hopfield networks with mixed delays and reaction-diffusion.Third,we relax the restrictions on some functions,extend the results of the pth-moment stability and almost everywhere stability under a general reference function,the conclusions are more general.Finally,we compare the results about the mean square stability.