On Synchronization Control For Fractional-Order Coupled Reaction-Diffusion Neural Networks

Recently,the research of dynamic analysis and synchronization control of fractional-order coupled neural network has become a hot topic of theoretical research and engineering application at home and abroad.However,reaction diffusion is neglected in the most of the published results on the fractional-order coupled neural network.In fact,reaction diffusion phenomenon cannot be avoided once the electrons moves in the inhomogeneous electromagnetic field in the simulation process of the artificial neural networks.Therefore,the dynamic behavior and synchronization control of fractional-order coupled reaction-diffusion neural networks is more meaningful in reality and valuable in application.This dissertation is mainly concerned with the synchronization of fractional-order coupled reaction-diffusion neural networks with different types of coupling weights by means of fractional differential equation theory,control theory and graph theory.The synchronization control is discussed in the first part for a type of fractionalorder coupled reaction-diffusion neural network with constant coupling weights.Firstly,based on the degree of network nodes,a pinning feedback control scheme is designed.In addition,the theory of fractional differential equations and the established fractional-order inequality are employed to obtain the criteria for realizing Mittag-Leffler synchronization.Furthermore,to reduce the control cost,the pinning fractional-order adaptive update strategies are designed in the definition of Caputo derivative and Caputo partial derivative to update time-varying control gains and control gains dependent on both time and space respectively.Finally,a numerical example is given to verify the correctness and effectiveness of the proposed control strategy and the proposed synchronization criteria.In the second part,the asymptotic synchronization is investigated for a class of fractional-order coupled reaction-diffusion neural networks with time-varying coupling weights is investigated.Firstly,for the time-varying weight of each edge in the network,a fractional-order adaptive scheme is established based on the Caputo derivative.Some criteria for asymptotic synchronization of the network are obtained with the help of the established fractional-order differential inequalities.It is noted that it is time-consuming and labor-consuming if each edge is controlled in real networks.In view of this,the pinning adaptive strategy is also discussed in the part.Some synchronization criteria are established by designing the adaptive update strategy only for the edge weights in a spanning tree.Finally,the feasibility of the theoretical results is verified by concrete examples.Considering the spatio-temporal characteristics of coupled neural networks,the spatio-temporal coupling weights,i.e.the coupling weights depending on both time and space factors,are introduced into the coupled networks,the synchronization control are investigated for fractional-order coupled reaction-diffusion neural networks with spatio-temporal coupling weights.Under the framework of Caputo partial derivative,the asymptotic synchronization of coupled networks is discussed basd on the designed fractional-order adaptive strategy and the pinning adaptive strategy respectively,and the relevant synchronization criteria are derived.It is worth noting that this is the first time to introduce spatio-temporal coupled weights into coupled reaction-diffusion neural networks.Finally,numerical simulation results are given to further verify the feasibility of the theoretical results.