Synchronization Analysis And Control For Coupled Reaction-diffusion Neural Networks

Synchronization is a natural phenomenon that exists widely in nature and reflects the way in which individuals achieve a certain purpose through information exchange.Researchers in various fields have revealed the mechanism of synchronization from different perspectives and applied them to practical projects to solve specific problems.The theory and practice show that the synchronizable coupled neural networks can help to design chaotic-based secure communication system and to solve the global minimum of non-convex objective function.Therefore,the study on synchronization analysis and control for coupled neural network have theoretical and practical significance.This dissertation reveals the effects of time delay,parameter uncertainty,disturbance,and parameter mismatch on the synchronization from two perspectives of analysis and control.This dissertation is divided into six chapters,the details are as follows:The first chapter introduces the related backgrounds and significance of neural network,the development tendency on synchronization of complex dynamic networks,and describes the current research situtation on synchronization of the coupled neural network.The main contents and arrangements of this dissertation are also explained according to the above analysis.In the second chapter,the influence of delay on the synchronization of coupled reaction-neural networks is studied.A kind of reaction-diffusion neural network model with time-varying state delays and coupling delays is proposed.Different from the existing one,the assumption posed on the delays in this chapter is very weak and can be time-varying,heterogeneous and unbounded.To overcome the difficulties caused by this kind of delay as well as diffusion effects,a comparison-based approach is proposed and a series of algebraic criteria for global asymptotic synchronization are obtained.By specifying the existing delays,some M-matrix-based criteria are derived to justify power-rate synchronization and exponential synchronization.In addition,new criterion on synchronization of general connected neural networks without diffusion term is also given,which is less conservative than the existing criterion in some cases.In the third chapter,the adaptive synchronization issue of coupled reaction-diffusion neural networks with directed topology is investigated.Due to the complexity of the network structure and the existence of spatial variables,it is very difficult to design proper adaptive strategies on coupling weights to achieve synchronization.Under the assumptions of two kinds of special network structures,that is directed spanning path and directed spanning tree,some novel edge-based adaptive strategies are proposed.By constructing a suitable energy function and using the Barbalat lemma,the correctness of the algorithm is proved theoretically.Compared with existing designs with fixed coupling strengths,the design of time-varying coupling strength is more in line with biological characteristics,and can avoid the introduction of global information.In the fourth chapter,the tracking synchronization problem for a class of coupled reaction-diffusion neural networks is studied.For the case where the tracking trajectory has identical individual dynamic with the network nodes,the edge-based and vertex-based adaptive strategies are respectively designed,and these adaptive strategies only need the local neighborhood information of the nodes,and thus are distributed.Meanwhile,for the case where the tracking trajectory has different individual dynamic with the network nodes,the vertex-based adaptive strategy is proposed to drive the synchronization error to a relatively small area which is adjustable according to the parameters of adaptive strategy.In the fifth chapter,the tracking synchronization problem of non-identically coupled reaction-diffusion neural networks with unknown parameters is studied.As the individual dyanmics of non-identically coupled reaction-diffusion neural networks are different from each other,it is very difficult to achieve accurate asymptotic synchronization.Meanwhile,parameter uncertainty leads to the failure of existing parameter-based control strategies.In this chapter,for the two cases that the state of tracking trajectory is bounded or unbounded,corrsponding adaptive control strategies are proposed to drive the synchronization error to a relatively small bounded area via robust adaptive control techniques,and the upper bound of the area is adjustable according to the parameters of adaptive strategies.The last chapter summarizes the research work of this dissertation.Furthermore,some prospects on the future work are also presented.