Study On Stability And Application Of Dynamic Neural Networks

It has been 40 years since neural networks were first introduced. In chapter one of this paper,neural networks' development history is summarized and emphasis is current development situation of dynamic neural networks.Because of dynamic neural networks' brilliant application prospect on associative memory,optimization,image processing and so on,many physicians,mathematicians et. are devoted to the study on this field. But all the models of neural networks before are assumed that self-feedback is linear which can not reflect the essentiality of the neural networks. So in chapter two of this paper,the self-feedback is improved and can be nonlinear. Moreover,basic features of this kind of neural networks are investigated. Two different methods are used in chapter two to analyze the features. First by introducing nonlinear measures,the existence,uniqueness and global exponential stability of the equilibrium point of this kind of neural networks are investigated. Two different Lipschitz continuous activations are considered. Some sufficient conditions and convergence estimate for global exponential stability of neural networks are obtained on condition that self-feedback is nonlinear. Second by using Liapunov direct method,two different sufficient global exponential stability conditions are obtained on condition that activation functions are Lipschitz continuous.So far,the most widely used neural networks are classified into two groups:continuous and discrete networks. However,in the real world there are many networks which belong to neither of the groups mentioned above. They are characterized by abrupt changes of states at certain instants. Many sudden and sharp changes occur in the form of impulses. Therefore it is important to investigate impulsive networks. Based on the structure of the dynamic neural networks,in chapter three of this paper the delayed impulsive neural network model is introduced. Based on analysis,sufficient conditions which ensure the exponential stability of this new neural networks are obtained.At last,in chapter four,several sufficient conditions which ensure theexponential stability of neural networks are used to solve optimization problems. By computing specific examples,it is found that those sufficient conditions are effective in solving optimization problems.