Stability Of Several Classes Of Continuous Hopfield Neural Networks

Hopfield neural network is a single-layer feedback neural network,which is widely used in image processing,associative memory,pattern classification and combinatorial optimization.Most of these applications depend on the qualitative behavior of the system,such as stability,convergence and oscillation.Stability is a main problem in the design and application of Hopfield neural network.In practical applications,neural networks often have time delays and impulses in the operation process,which will interfere with the stability of neural networks.Therefore,it is necessary and practical to study Hopfield neural networks with time delays and impulse.In this thesis,the stability of three kinds of continuous Hopfield neural networks are discussed by using generalized norm properties,fixed point theorem,matrix spectral radius theory,construction of Lyapunov functional and inequality analysis technology.In Chapter 1,this part briefly introduces the development and research status of Hopfield neural network,and analyzes the research status of Hopfield neural network stability.In Chapter 2,according to the properties of three generalized norms and the method of constructing Lyapunov functional,the existence and uniqueness of the equilibrium point of Hopfield neural network with constant delay and time-varying delay will be proved,and the sufficient conditions for the global exponential stability of the system are obtained.In Chapter 3,the impulsive Hopfield neural network model with mixed delays is studied.The existence and uniqueness of the equilibrium point of the model are proved by using the fixed point theorem.Then,by constructing the lyaunov method,the sufficient conditions for determining the global exponential stability of the equilibrium point of the system are obtained.In Chapter 4,fractional Hopfield neural networks with constant delay and proportional delay are studied.Firstly,the generalized Gronwall inequality with delay is constructed by using Gronwall inequality.Then,the sufficient conditions for the finite time stability of the system are obtained by using Caputo derivative properties,some important inequalities and the generalized Gronwall inequality with delay.The chapter 5,summarizes and prospects the previous chapters,and puts forward the direction of follow-up research on the basis of this thesis.