Asymptotic behaviors in a transiently chaotic neural network

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July 2004, 10(3): 805-826. doi: 10.3934/dcds.2004.10.805

Asymptotic behaviors in a transiently chaotic neural network

Shyan-Shiou Chen ^1, and Chih-Wen Shih ^1,

1.	Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan, Taiwan

Received January 2002 Revised May 2003 Published January 2004

Abstract
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We are interested in the asymptotic behaviors of a discrete-time neural network. This network admits transiently chaotic behaviors which provide global searching ability in solving combinatorial optimization problems. As the system evolves, the variables corresponding to temperature in the annealing process decrease, and the chaotic behaviors vanish. We shall find sufficient conditions under which evolutions for the system converge to a fixed point of the system. Attracting sets and uniqueness of fixed point for the system are also addressed. Moreover, we extend the theory to the neural networks with cycle-symmetric coupling weights and other output functions. An application of this annealing process in solving travelling salesman problems is illustrated.

Keywords: Lyapunov function, Neural network, convergence of dynamics..

Mathematics Subject Classification: 92B20, 39A1.

Citation: Shyan-Shiou Chen, Chih-Wen Shih. Asymptotic behaviors in a transiently chaotic neural network. Discrete & Continuous Dynamical Systems - A, 2004, 10 (3) : 805-826. doi: 10.3934/dcds.2004.10.805

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