Stochastic And Impulsive Exponential Stability Analysis Of Hopfield Neural Networks With Delays

In recent decades years, some of reasons why Hopfield neural works have received a great deal of attention of physics,mathematics engineers,Biological,and computer workers etc. are because of it can be applied to signal and image processing ect.. As we all know, the phenomenon of delay or stochastic or impulsive is an unavoidable in practical application, and the delay or stochastic or impulsive has a huge influence on stability of the neural network. Some neural network system without delay is stable, however, neural networks were introduced to delay or stochastic or impulsive, the stability of the original neural networks system becomes unstable, so structure of neural network system change in essence, and stability analysis of neural networks with delay or stochastic or impulsive becomes more difficult. There are usually two ways to research on the stability of neural network: Firstly, near balance of neural network system was linear, so conditions of the local stability of neural network was obtained in this way. Secondly, by employing appropriate Liapunov function, stability or global exponential stability of neural network was obtained.In the paper, the global exponential stability of a classes of impulsive neural networks with delayed and two different stochastic Hopfield neural network with delayed are mainly studies. A series of new exponential stability results are obtained. Specifically, this paper covers the following four aspects :1,We briefly outline the significance,background,progress,application prospects of the neural network of the achievements of previous studies on this.2,In this chapter, the global exponential stability of impulsive Hopfield neural network with variable delay is discussed. Apply Young inequality,method of Liapunov functionals ect., some new gloabl exponential stability results are obtained, which have been compared with the results of global exponential stability of the previous literature that the conditions required more relaxed, our results are less restrictive than previously known criteria, and we study neural networks that activation functions of neural networks are not neither differentiability nor strict monotonicity or unbounded. Moreover, we further extend and improve the results of the recent results of the relevant literature.3,The mean square exponential stability of stochastic interval Hopfield neural network model with Markov chain and variable delay is studied. To address the difficulties arising from the variable delay changed. In the paper, by employing Markov,interval matrix inequality,Holder inequality,Liapunov function methods and skills ect., several new exponential stability criteria are established. Even if the results has been established exponential stability for the general Hopfield network with delay. Moreover, these theories can be applied to the control system,general neural networks system and biological nervous system ect..4,The mean square exponential stability of stochastic of high Hopfield neural network model with reaction-diffusion and variable delay is deeply studied. By employing the LIM matrices,Halanay inequality,boundary conditions,Liapunov functional method and Non-negative Semimartingale Convergence Theorem ect., several new exponential stability criteria are established. Furthermore, our results are allowed to have a wider choice for the activation functions, including the usual sigmoid functions and the piecewise-linear functions ect.. Meanwhile, the methods were more suitable for Not only stochastic recurrent neural network with delayed and reaction-diffusion, but also general stochastic neural network with delay.