Wavelet chaotic neural network with nonlinear self-feedback and its application

Abstract

Wavelet chaotic neural network is a kind of chaotic neural network with non-monotonous activation function composed by Sigmoid and Wavelet. In this paper, wavelet chaotic neural network models with different nonlinear self-feedbacks are proposed and the effects of the different self-feedbacks on simulated annealing are analyzed respectively. Then the proposed models are applied to the 10-city traveling salesman problem (TSP) and by comparison the performance of the model with wavelet self-feedback is superior to that of the rest others presented in this paper. Moreover, the performance of the model with wavelet self-feedback is improved by the scale index and the location index of the wavelet. Finally, the dynamics of an internal state of the model for the 10-city TSP is researched, including chaotic area distribution, the largest Lyapunov exponents and the effects of the chaotic distribution on the performance of the network for 10-city TSP. The numerical simulations show that the models can converge to the global minimum or approximate solutions more efficiently than the Hopfield network, and the performance of the model with wavelet self-feedback is superior to that of the others presented in this paper.