Morlet Wavelet chaotic neural networks with random noise

Chaotic neural networks have been proved to be powerful tools to solve the optimization problems. Based on a chaotic neural network with random noise, a new chaotic neural network model with random noise called Morlet Wavelet chaotic neural network was presented, and the chaotic mechanism was introduced by the attenuation of the self-feedback connection weight. The activation function of the new model is non-monotonous, which is composed of sigmoid and Morlet Wavelet. First, the figures of the reversed bifurcation and the maximal Lyapunov exponents of single neural unit were given. Second, the new model was applied to solve function optimizations. Finally, 10-city traveling salesman problem was given and simultaneously the parameters of the network in solving the 10-city traveling salesman problem were given. The effects of the non-monotonous degree in the model on solving the 10-city traveling salesman problem were discussed. The new model can solve the 10-city traveling salesman problem more effectively because of Morlet wavelet being a kind of basic function. Seen from the simulation results, the new model is powerful.