Asymptotic Stability And Passivity Of Several Classes Neural Networks With Proportional Delay

Neural networks,as a kind of important mathematical model,which has important applica-tions in many practical problems,such as information processing,pattern recognition,intelligent control,nonlinear optimization,evaluation and prediction,and so on.At the same time these applications require the network to meet some dynamic behavior,analysis of dynamical behaviors is an absolutely necessary step for practical excogitation of high-quality neural networks.Thus,it is necessary to study the dynamic behaviors of neural networks.In addition,due to the finite switching speed of information processing and the inherent.communication time of neurons,time delay is unavoidable in the process of signal transmission of real system,and its existence may result in oscillation,chaos and instability of the system.Proportional delay is a.kind of unbounded delay,it s characteristic is that.the operation time of the network can be mastered according to the maximum time delay allowed by the network.Therefore.it is of great theoretical value and practical significance to investigate the dynamic behaviors of neural networks with proportional delays.In this paper,we mainly discuss the global asymptotic stability of a class of cellular neural networks with proportional delay and the passivity of the two kinds of coupled reaction-diffusion neural networks with proportional delay.In the first part,according to the sequence of neural networks,delayed neural networks,neural networks with proportional delay,cellular neural networks and coupled reaction-diffusion neural networks,the development process and research status of them are introduced in detail.In the second part,the global asymptotic stability of a class of cellular neural networks with proportional delay is discussed.By utilizing Homeomorphic mapping theorem as well as con-structing an appropriate Lyapunov functional,a sufficient condition is derived for the existence,uniqueness and global asymptotic stability of the equilibrium point.In the third part,the passivity of a class of coupled reac tion-diffusion neural network with im-pulsive effects and proportional delay is introduced.By establishing proper Lyapunov fuuctionals,taking advantage of inequality techniques and the Kronecker product's properties,sufficient condi-tions for the network to achieve input-strictly passivity and output-strictly passivity are obtained.In the fourth part,we mainly study the passivity of a class of coupled reaction-diffusion neural networks with adaptive coupling strength and proportional delay.In order to actualize the passivity of the system under consideration,we design the adaptive strategy to adjust the coupling strength between nodes.And then by constructing suitable Lyapunov functionals,combining with the analysis technique of inequality and Kronecker product s properties,some sufficient conditions are acquired for passivity of the system.The results obtained in this paper are completely new.and the corresponding numerical ex-amples and their simulation results are given in each chapter.and the correctness and feasibility of the theoretical results are further verified.