Research And Application Of The Wavelet Chaotic Neural Network

The Artificial Neural Network has been developed for researching the congnitive progress of human, the central issues are the maching learning method of Object-oriented research and the structural problems of learning machine.The chaos is a behave of intrinsic random process in nonlinear uncertain system, the chaotic system is a nonlinear dynamics system, and the structure of Hopfield can combine the Neural Network and the behavior of the nonlinear dynamic,so it can be used as the network architecture model to research the Chaotic Neural Network.The Wavelet Analysis is a rapid developing new field of math, also has double meaning in profound theory and wide range application. Compared to the Fourier Transform, the Wavelet Transform is a local analysis of time(space) frequency. Through the operation of companding and offset, it does Multi-scale refinement to signal step by step, and it meets the need of Time-Frequency Signal Analysis, it can focus on any details of signal.We did more research about the output function of the Chaotic Neural ,Network,also introduced the characters of chaos and the basic characters of the Chaotic Neural Network, did some research on constructive method and character of the Chaotic Neural Network and application in combinatorial optimization.Based on the previous researches, we proposed a new Wavelet Chaotic Neuron, it also can be called the Mexican Hat Wavelet Chaotic Neuron .Its activative function is the combination of Mexican Hat Wavelet function and Sigmoid function, and did some research about the Choatic characters of this Neuron. Based on this Neuron, we proposed a new Neural Network called the Mexican Hat Wavelet Chaotic Neural Network(MWCNN), MWCNN has the superiorities of Wavelet, Chaos and Neural Network, that can make it more powerful on global optimum search and on Function Approximation. We also did research about its applications of combinatorial optimization and chaotic time series prediction, and simulated its applications, the simulated results show that the MWCNN's abilities of combinatorial optimization and Function Approximation are more powerful than the Transient Chaotic Neural Network.