Chaotic pulses for discrete reaction diffusion systems

Yasumasa Nishiura, Daishin Ueyama, Tatsuo Yanagita

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

Abstract

Existence and dynamics of chaotic pulses on a one-dimensional lattice are discussed. Traveling pulses arise typically in reaction diffusion systems like the FitzHugh-Nagumo equations. Such pulses annihilate when they collide with each other. A new type of traveling pulse has been found recently in many systems where pulses bounce off like elastic balls. We consider the behavior of such a localized pattern on one-dimensional lattice, i.e., an infinite system of ODEs with nearest interaction of diffusive type. Besides the usual standing and traveling pulses, a new type of localized pattern, which moves chaotically on a lattice, is found numerically. Employing the strength of diffusive interaction as a bifurcation parameter, it is found that the route from standing pulse to chaotic pulse is of intermittent type. If two chaotic pulses collide with appropriate timing, they form a periodic oscillating pulse called a molecular pulse. Interaction among many chaotic pulses is also studied numerically.

Original languageEnglish
Pages (from-to)733-754
Number of pages22
JournalSIAM Journal on Applied Dynamical Systems
Volume4
Issue number3
DOIs
Publication statusPublished - 2005

Keywords

  • Bifurcation theory
  • Chaos
  • Dissipative systems
  • Lattice differential equation (LDE)
  • Localized pulse

ASJC Scopus subject areas

  • Analysis
  • Modelling and Simulation

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