Comparative study of chaotic neural networks with different models of chaotic noise

Abstract

In order to explore the search mechanism of chaotic neural network(CNN), this paper first investigates the time evolutions of four chaotic noise models, namely Logistic map, Circle map, Henon map, and a Special Two-Dimension (2-D) Discrete Chaotic System. Second, based on the CNN proposed by Y. He, we obtain three alternate CNN through replacing the chaotic noise source (Logistic map) with Circle map, Henon map, and a Special 2-D Discrete Chaotic System. Third, We apply all of them to TSP with 4-city and TSP with 10-city, respectively. The time evolutions of energy functions and outputs of typical neurons for each model are obtained in terms of TSP with 4-city. The rate of global optimization(GM) for TSP with 10-city are shown in tables by changing chaotic noise scaling parameter γ and decreasing speed parameter β. Finally, the features and effectiveness of four models are discussed and evaluated according to the simulation results. We confirm that the chaotic noise with the symmetry structure property of reverse bifurcation is necessary for chaotic neural network to search efficiently, and the performance of the CNN may depend on the nature of the chaotic noise. © Springer-Verlag Berlin Heidelberg 2005.