### Abstract

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.

Original language | English |
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Pages (from-to) | 805-826 |

Number of pages | 22 |

Journal | Discrete and Continuous Dynamical Systems |

Volume | 10 |

Issue number | 3 |

Publication status | Published - 2004 Apr 1 |

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### Keywords

- Convergence of dynamics
- Lyapunov function
- Neural network

### ASJC Scopus subject areas

- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discrete and Continuous Dynamical Systems*,

*10*(3), 805-826.