The Research Of The Stability Of The Neural Network Based On The Nonsmooth Anaslysis

Since the Hopfield firstly put forward the concept of energy function to study the neural network model and realized circuit, the qualitative research about the stability never interrupted. Also the research about the stability of the neural network has important theoretical and practical significance.Based on activation functions of the neural network satisfy the Lipschitz continuous and inverse Lipschitz continuous, Our paper from the perspective of nonsmooth analysis discusses the promblemabout the stability of the neural network. Main tasks are as follows:Firstly, the main background and the recent development are described for the artificial neural network ,the dynamic properties of the neural network,the research methods and the content are also introduced. Secondly, the artificial neural networks and biological neural networks are compared, explained the working principle of the artificial neural networks, and the common neural network model. Thirdly, a class of the delayed cellular neural network with Lipschitz activation functionis discussed. On the based of th research of the previous stability of the neural networks, used the Lipschitz properties of the function to extend the activation function of the neural networks appropriately, and using the nonsmooth analysis method, a new criterion of the existence, uniqueness and global asymptotic stability of a Class of Neural Networks are given, and a numerical example demonstrates the feasibility of the conclusions. Finally, the bidirectional associative memory model with inverse Lipschitz activation function are discussed. Using the nonsmooth analysis, topological degree methods and the properties of Lyapunov functions obtained a new robust stability criterion of the bidirectional associative memory neural networks, while a numerical example is given to show the validity of the conclusion.