Synchronous Analysis And Control Of Multi-coupled Fractional-Order Reaction-Diffusion Neural Network

As is well known,neural networks(NNs)can be implemented in electronic circuits,and electrons move in uneven electromagnetic fields to produce reaction diffusion phenomenon.Therefore,the reaction-diffusion phenomenon can not be ignored in NNs.With the development of fractional order theory,fractional-order reactiondiffusion NNs(FORDNNs)has been studied by some authors.Several FORDNNs can couple to each other to form a coupled FORDNNs(CFORDNNs).The CFORDNNs not only has the properties of FORDNNs,but also shows more complex dynamic behaviors that a single FORDNNs does not have.Therefore,it is valuable to discuss the dynamic behavior of CFORDNNs.However,the dynamic behavior of CFORDNNs has only been studied by a few authors.On the other hand,due to the diversity of influencing factors,the dynamic behavior of multiple CFORDNNs(MCFORDNNs)should be studied.In this paper,two types of MCFORDNNs are proposed respectively.In chapter one,the research background of MCFORDNNs and and the significance of studying MCFORDNNs.In chapter two,the synchronization and adaptive synchronization of CFORDNNs with multiple state couplings are discussed.By using Laplace inverse transform and some inequality techniques,several sufficient conditions are given to ensure the synchronization of the proposed network models.Finally,a numerical example and its simulation results are used to prove the effectiveness of the proposed adaptive control scheme.In chapter three,the synchronization and adaptive synchronization of CFORDNNs with multiple spatial diffusion couplings are studied,and several sufficient conditions to ensure the synchronization of the models are given.Finally,the effectiveness of the proposed adaptive control scheme is verified.The chapter four is the summary of this paper and the prospect of future research work.