The Control And Synchronization Of Several Class Of Reaction-Diffusion Neural Networks

The control and synchronization of reaction-diffusion neural networks are cen-tral topics in the investigation of the dynamics of neural networks,and have been received much attention by a lot of international and domestic academics.In this master's degree thesis,by constructing different discrete controllers,pinning impul-sive stabilization for BAM reaction-diffusion neural networks with mixed delays,intermittent sampled-data synchronization of hybrid coupled reaction-diffusion neu-ral networks with time delays,as well as adaptive intermittent synchronization of coupled reaction-diffusion neural networks with switching topology are studied,re-spectively.The main works in this paper can be summarized as follows:The first section is introduction,in which we present the research background and the research status of the dynamics of reaction-diffusion neural networks.In this section,some common methods of control and synchronization as well as the research contents of this thesis are also be introduced.In section 2,the BAM reaction-diffusion neural networks with mixed delays are stabilized exponentially by a pinning impulsive control,in which the control func-tions are nonlinear and the pinning neurons are determined by reordering the state error.In addition,based on the designed control protocol and Lyapunov function approach,some novel and useful criteria,which depend on the diffusion coefficients and controlling parameters,are established to guarantee the global exponential sta-bilization of the considered neural networks.Finally,two examples are given to demonstrate the effectiveness of the proposed method.In section 3,by introducing an intermittent control with spacial sampled-data,the exponential synchronization of hybrid coupled reaction-diffusion neural networks with mixed delays is discussed,and some sufficient conditions,which depend on time delays,diffusion coefficients and coupled strengths,are established to guarantee the synchronization of the networks.This intermittent sampled-data control not only unifies the periodic intermittent control and the aperiodic case,but also is intermit-tent in time and data sampling in space.One simulation example is presented in the end of this section to demonstrate the feasibility and effectiveness of intermittent control with spacial sampled-data.In section 4,by constructing suitable intermittent controllers with constant control gains and adaptive control gains,respectively,the synchronization problem of linearly coupled reaction-diffusion neural networks with switching topology is discussed,and some criteria depended on diffusion coefficients and coupled strengths are established to guarantee the synchronization of the networks.Moreover,the adaptive control gains in the controller are dependent on space as well as time.Finally,the main results of this section are simulated by data.