Control And Synchronization Of A Class Of Neural Network Model

The importance of the study of the neural network system theory has beenrecognized by many scientists, and lots of constructive results have been obtained tillnow. Many people considered that the neural network theory study must be amainstream direction for the future development of computer, but its development is notclearly, and it has lots of problems. Since the problem of the Hopfield model wasprovided by1980s, the theory of neural network system has once again aroused theinterest of scientists and become a focus of the modern science. From the mid-1980s toearly1990s, the development of the theory of neural network system is very rapid,many applied models appeared. During the study of these models, we find that some ofthem are not well resolved, such as network structure model of the human nervoussystem and information processing functions data description and so on. Hence, we willinvestigate further on two of these models in this paper.Firstly, the existing research results of several neural network models are introduced,the generation, development and significance about the control and synchronization ofneural network models are given, the framework of the organization of this paper islisted.Secondly, we analysis and discuss in-depthly on a kind of Hopfield neural networkwith time delay. A new class of Liapunov functional which contains a tripe-integralterm is constructed to derive some new delay-dependent stability criteria. The obtainedcriteria are less conservative because free-weighting matrices method and a convexoptimization approach are considered. Finally, numerical examples are given toillustrate the effectiveness of the proposed method.Finally, we discuss the global exponential stability of a class of BAM neuralnetworks with mixed delays under impulsive control. Based on Homeomorphism theoryand inequality technique, the existence and uniqueness of the equilibrium point arestudied. By using the Liapnuov functional method, the global exponential stability ofthe equilibrium point under impulse control is investigated. Finally, an example toillustrate the effectiveness of existing results.