Passivity And Synchronization Of Three Classes Of Multi-weight Coupled Reaction-diffusion Neural Networks

More recently,the dynamic behaviors of neural networks(NNs)have triggered increased attention for the reason of their extensive applications in image processing,pattern classification,optimization and so on.As is well known,the movement of electrons in a nonuniform electromagnetic field can result in the phenomenon of reaction diffusion.Therefore,reaction diffusion phenomenon should be taken into account in the neural networks.Up to now,the dynamical behaviors of reactiondiffusion neural networks(RDNNs)have attracted a great deal of attention of many researchers.Moreover,coupled RDNNs(CRDNNs),composed of multiple nonidentical or identical RDNNs,has been paid more and more attention in various fields due to their diversity of applications in harmonic oscillation generation,chaotic generator design and pattern recognition,etc..Consequently,it is very important to consider the passivity and synchronization of CRDNNs.On the other side,in the RDNNs,not only different diffusion of node has a great influence on other nodes,but also different time derivatives of node may give rise to different changes of its neighbor nodes.Therefore,it is very worthwhile considering the passivity and synchronization for CRDNNs with spatial diffusion coupling and derivative coupling.Furthermore,for some real-life networks such as urban population flow networks,food webs,etc.,they may be better represented by complex networks with multiple weights(CNMWs).Unfortunately,very few authors discussed the passivity and synchronizartion of CRDNNs with multiple state couplings,multiple spatial diffusion couplings and multiple derivative couplings.In addition,the networks themselves cannot achieve desired dynamical behaviors(such as passivity and synchronization)in many circumstances.Generally speaking,a complex network consists of large number of interconnected nodes,thus it is impossible to design controller for every node.Consequently,some authors have developed several pinning control strategies for ensuring the passivity and synchronization of CRDNNs.To our best knowledge,the passivity and synchronization for CRDNNs with multiple derivative couplings have not been considered.This paper respectively studies the adaptive passivity and synchronization of CRDNNs with multiple state couplings or multiple spatial diffusion couplings,and discusses the analysis and pinning control for passivity and synchronization of multiple derivative coupled reaction-diffusion neural networks.In the chapter II,two types of coupled reaction-diffusion neural networks with multiple state couplings or spatial diffusion couplings are presented.By selecting appropriate adaptive control schemes and employing inequality techniques,several passivity conditions for these network models are given.In addition,two sufficient conditions for ensuring the synchronization of the proposed network models are also established by exploiting the output-strictly passivity.In the chapter III,a class of multiple derivative coupled reaction-diffusion neural networks with and without parameter uncertainties is investigated.Firstly,by using inequality techniques,the passivity and synchronization of the proposed network models are analyzed,and several criteria are derived.Furthermore,a pinning control strategy is also developed to ensure that these networks can achieve passivity and synchronization.Finally,some numerical examples are presented to verify the effectiveness of the obtained criteria.