Research On Nonlinear Self-Feedback Chaotic Neural Networks And Their Applications

The self-feedback chaotic neural network's structure is similar to that of Hopfield neural network, and it has transient chaotic response. By combining chaotic dynamics and converging dynamics together, the neural network transit gradually to Hopfield neural network is made. By introducing converging factor, the aim of controlling chaos is attained. Unlike the gradient descent neural network, the self-feedback chaotic neural network has more complex dynamics property, and diversified attractor exist. It is just the dynamics that make it possible for the network to be a technology with abroad application foreground for information processing and optimization computation.According to the representative literature since the generation of the chaotic neural network, the development and the model of the chaotic neural network are systematically introduced and the mechanisms of the chaos arising from and the characteristics of the different models are analyzed. On this basis, antitrigonometric function self-feedback chaotic neural network, sigmoid function self-feedback chaotic neural network and morlet wavelet function self-feedback chaotic neural network are proposed. Compared to the previous linear self-feedback chaotic neural network, the introduction of the nonlinear self-feedback term makes that chaotic neural network has more complex dynamics property and the network's internal state has more complex chaotic search property.Antitrigonometric function self-feedback chaotic neural network, sigmoid function self-feedback chaotic neural network and morlet wavelet function self-feedback chaotic neural network have nonlinear self-feedback property, This paper researches the behavior of the networks' single chaotic neural unit. Present a new chaotic neuron's dynamic system unit which can make the chaotic searching permanent and make a research of the Lyapunov exponent. Study the stability of the energy function of this network with emphasis, and obtain the necessary and sufficient conditions of asymptotic stability which indicate this network is asymptotic stable under certain conditions.Simultaneously antitrigonometric function self-feedback chaotic neural network, sigmoid function self-feedback chaotic neural network and morlet wavelet function self-feedback chaotic neural network are used for solving function optimization problem and10-city TSP, and compares it with the other solution methods of Hopfield neural network and Chen's chaotic neural network. The results indicate that the antitrigonometric function self-feedback chaotic neural network, sigmoid function self-feedback chaotic neural network and morlet wavelet function self-feedback chaotic neural network have better optimization ability.