Transversal homoclinic orbits in a transiently chaotic neural network

Shyan Shiou Chen, Chih Wen Shih

Research output: Contribution to journalArticle

17 Citations (Scopus)

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
Publication statusPublished - 2002 Sep

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Chaotic Neural Network
Homoclinic Orbit
Orbits
Neural networks
orbits
Combinatorial optimization
Chaos theory
Annealing
Numerical Range
chaos
Chaotic Dynamics
Chaotic Behavior
Combinatorial Optimization Problem
Chaos
Discrete-time
optimization
annealing
Fixed point
Neural Networks
Scenarios

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

Transversal homoclinic orbits in a transiently chaotic neural network. / Chen, Shyan Shiou; Shih, Chih Wen.

In: Chaos, Vol. 12, No. 3, 09.2002, p. 654-671.

Research output: Contribution to journalArticle

Chen, Shyan Shiou ; Shih, Chih Wen. / Transversal homoclinic orbits in a transiently chaotic neural network. In: Chaos. 2002 ; Vol. 12, No. 3. pp. 654-671.
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