Research Of Stability For Cellular Neural Networks With Time Delay

The neural network originated from the research of the nerve physiology, through simulates the sensing neurons of the human brain as well as the corres- ponding process, to establishment of the earliest mathematical model to start just a few dozens, has developed gradually for the application for a wide rang of new discipline. Moreover, it is further abstract and the simulation research in turn gives the nerve physiology of the research to inspiration and the new ideas. It is well known, the system often has the time delay during transmission. For easy to analyze and the application, when modelings many system has neglected this kind of time delay. But, the time delay is the objective existence. When introdu- ce the neural network time delay its stability analyses become very difficult. At the same time, the time delay existence also brings the influence to system's stability, has produce shock behavior or other instability, and even presents the chaos phenomenon. Therefore, it is especially important to study the system's stability.The paper mainly divided into two parts:The first part is the basic part of the paper. First, we give the simple introduction to the cell neural network. Next, we introduce the neural network development historical survey of overview of the history and the research present situation. Finally, it has carried on the analysis summary to the neural network stable theorem and the definition.The second part is the main part of the paper. Including the third chapter, the fourth chapter and the fifth chapter, the main results are in the third chapter. It uses four theorems to study the stability of two kinds of discrete and distribution time-delay neural network model, based on the Lyapunov function and the linear matrix inequality (LMI) tools as well as MATLAB toolbox and so on, it takes the stability problem becomes some function which proper defined on the path's of the system, these functional obtains the corresponding stable condition through these, even is the global stability condition, received some new results, and explained its effectiveness and the feasibility by numerical examples.