Exponential Stablity Of Numerical Solutions To Stochastic Delay Hopfield Neural Networks With Jumps

In this paper,it is considered for a class of stochastic delay Hopfield neural networkswith Poisson jumps.The main content of the thesis is to investigate the MS-stability of theEuler method,the GMS-stability of the semi-implicit Euler method for this equation andmean square exponential stability of the semi-implicit Euler method.The thesis is organized as follows:In chapter 1, we briefly introduce some basic knowledge about neural networksand research status of Hopfield neural networks,the significance of the subject is alsointroduced.In chapter2, we introduce the model of stochastic delay Hopfield neural networks withjumps and collect some basic preliminaries which are essential and then give the sufficientcriteria which ensure the analytical solution is exponentially stable in mean square.In chapter3, we prove the MS-stability of the Euler method applied to stochastic delayHopfield neural networks with jumps.In chapter4, we prove the GMS-stability and exponential stability in mean square of thesemi-implicit Euler method applied to stochastic delay Hopfield neural networks withjumps.In chapter5, some examples are provided to illustrate our theory.