Asymptotic Behavior For Stochastic Reaction Diffusion Hopfield Neural Network With Delays

In this paper, we study the asymptotic behavior for different kinds of stochasticreaction diffusion Hopfield neural network with delay, and this dissertation is dividedinto6parts.In the first chapter, we not only review history and present situation of researchon the neural network, but also explain theoretical significance and practical valueto the research of neural network. Moreover, We will discuss the new phenomenonsaccompanying the occurrence of delay, reaction-diffusion term as well as stochas-tic disturbance, meanwhile the corresponding mathematical difficulties that we willmeet will be given in this chapter.In the second chapter, we focus on the long time behavior of the mild solution fordelayed reaction-diffusion Hopfield neural networks driven by infinite dimensionalWiener processes. We will first study the existence and uniqueness of the mild so-lution for this system. Afterwards we will prove the stochastic exponential stabilityof this system. An example is given to examine the availability of the results of thispaper, simulations is also given by using the Matlab.In the third chapter, we study the asymptotic behavior for a class of delayedreaction-diffusion Hopfield neural networks driven by finite dimensional Wiener pro-cesses. Some new sufficient conditions are established to guarantee the mean squareexponential stability of this system by using Poincare′’s inequality and stochasticanalysis technique. The proof of the almost surely exponential stability for this sys-tem is carried out by using the Burkholder-Davis-Gundy inequality, the Chebyshevinequality as well as the Borel-Cantelli lemma. Finally, an example is given to illus-trate the effectiveness of the proposed approach, and the simulation is also given byusing the Matlab.In the fourth chapter, we study the global existence and uniqueness of the mildsolution for reaction-diffusion Hopfield neural networks (RDHNN) driven by Wiener processes using a priori estimate, then the random attractor for this system is alsoestablished by constructing proper random dynamical system.In the fifth chapter, the sliding mode control problems of a class of Hopfield neu-ral networks with S-type distributed delays and reaction diffusion terms are investi-gated. First, the improved Hanalay inequality and norm inequality are presented.Then, the sliding mode equation is established by the equivalent control method,and the existence of the attracting sets and exponential stability of this system arediscussed by using the inequalities. Then the variable controller is designed, the ap-proximate time estimate from any initial state to sliding manifolds is also obtained.Finally, an example is given to prove the availability the result of this paper, and thesimulation is also given by using the Matlab.The prospect of our research will be given at last.