Dynamics for discrete-time cellular neural networks

Shyan Shiou Chen, Chih Wen Shih

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

This presentation investigates the dynamics of discrete-time cellular neural networks (DT-CNN). In contrast to classical neural networks that are mostly gradient-like systems, DT-CNN possesses both complete stability and chaotic behaviors as different parameters are considered. An energy-like function which decreases along orbits of DT-CNN as well as the existence of a globally attracting set are derived. Complete stability can then be concluded, with further analysis on the sets on which the energy function is constant. The formations of saturated stationary patterns for DT-CNN are shown to be analogous to the ones in continuous-time CNN. Thus, DT-CNN shares similar properties with continuous-time CNN. By confirming the existence of snap-back repellers, hence transversal homoclinic orbits, we also conclude that DT-CNN with certain parameters exhibits chaotic dynamics, according to the theorem by Marotto.

Original languageEnglish
Pages (from-to)2667-2687
Number of pages21
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume14
Issue number8
DOIs
Publication statusPublished - 2004 Aug

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Keywords

  • Cellular neural network
  • Chaos
  • Complete stability
  • Homoclinic orbits
  • Pattern formation
  • Snap-back repeller

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

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