Stability And Synchronization Analysis Of Continuous Hopfield Neural Networks

The extensive application of neural networks in various fields has made it to be a popular research topic for scholars.Hopfield neural network is a single layer fully connected feedback neural network,which is the most classic and widely used neural network in the feedback neural network model.Recently,Hopfield neural network has been applied into many fields,such as pattern recognition,image processing,system fault diagnosis,parameter estimation,and so on.With the development of Hopfield neural network theory,and theories,technologies related with Hopfield neural network,the application of Hopfield neural networks will be more and more widespread.In this paper,the stability and synchronization of Hopfield neural network is studied by means of differential inclusion theory,Lyapunov stability theory,indefinite point theorem,Mittag-Leffler function property,matrix measure,linear matrix inequality analysis technique and basic properties of inequality.The main research contents are summarized as follows:1.The global Mittag-Leffler stability analysis issue of fractional-order impulsive Hopfield neural networks is investigated.Under the conditions that the activation function satisfies two different conditions,the conditions of existence of the solution of the fractional-order impulsive Hopfield neural network are given by the fixed point theorem.Moreover,under the condition that the activation function satisfies the one-side Lipschitz condition,the conditions of the existence,uniqueness and global Mittag-Leffler stability of equilibrium point of the fractional-order impulsive Hopfield neural networks are put forward by means of contraction mapping principle and Lyapunov stability method,respectively.2.The global quasi-synchronization and global anti-synchronization issue of delayed Hopfield neural networks with discontinuous activations are addressed.Applying the Lyapunov-Krasovskii function with matrix measure and differential inclusion theory,the sufficient conditions are put forward to ensure that such delayed Hopfield neural networks with discontinuous activations drive system and response system are globalquasi-synchronized under the non-fragile additive controller.Furthermore,based on Lur'e-Postnikov Lyapunov function,differential inclusion theory and inequality analysis technique,the sufficient conditions to achieve the global anti-synchronization of the delayed Hopfield neural networks with discontinuous activations drive system and response system are proposed in term of the linear matrix inequalities.3.The robust pinning synchronization problem of fractional order Hopfield neural networks with uncertain parameters and discontinuous activation functions is analyzed.An appropriate linear controller is designed to ensure the error dynamical system get robust Mittag-Leffler stability via Lyapunov function approach and non-smooth analysis theory.At the same time,using inequality analysis techniques,the robust pinning synchronization conditions of fractional-order Hopfield neural network driven systems and response systems with uncertain parameters and discontinuous activation functions are given in terms of linear matrix inequality.4.The finite-time synchronization issue of fractional-order complex-valued Hopfield neural networks with time delay is analyzed.The sufficient conditions are presented to guarantee the finite-time synchronization of the fractional-order complex-valued delayed Hopfield neural networks when: 1/2???1 and 0???1/2(? is order)by properties of H(?)lder inequality and Gronwall inequality,and so on.