Transversal homoclinic orbits in a transiently chaotic neural network

Shyan Shiou Chen, Chih-Wen Shih*

*Corresponding author for this work

Research output: Contribution to journalArticle

17 Scopus citations

Abstract

We study the existence of snap-back repellers, hence the existence of transversal homoclinic orbits in a discrete-time neural network. Chaotic behaviors for the network system in the sense of Li and Yorke or Marotto can then be concluded. The result is established by analyzing the structures of the system and allocating suitable parameters in constructing the fixed points and their pre-images for the system. The investigation provides a theoretical confirmation on the scenario of transient chaos for the system. All the parameter conditions for the theory can be examined numerically. The numerical ranges for the parameters which yield chaotic dynamics and convergent dynamics provide significant information in the annealing process in solving combinatorial optimization problems using this transiently chaotic neural network.

Original languageEnglish
Pages (from-to)654-671
Number of pages18
JournalChaos
Volume12
Issue number3
DOIs
StatePublished - 1 Jan 2002

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