Chaotic pulses for discrete reaction diffusion systems

SIAM Journal on Applied Dynamical Systems Volume 4 Issue 3 Page 733-754 published_at 2005
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Title ( eng )
Chaotic pulses for discrete reaction diffusion systems
Creator
Nishiura Y
Ueyama Daishin
Yanagita T
Source Title
SIAM Journal on Applied Dynamical Systems
Volume 4
Issue 3
Start Page 733
End Page 754
Keywords
Bifurcation theory
Chaos
Dissipative systems
Lattice differential equation
LDE
Localized pulse
Descriptions
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.
NDC
Mathematics [ 410 ]
Language
eng
Resource Type journal article
Publisher
Society for Industrial and Applied Mathematics
Date of Issued 2005
Rights
Copyright (c) 2005 Society for Industrial and Applied Mathematics
Publish Type Author’s Original
Access Rights open access
Source Identifier
[ISSN] 1536-0040
[DOI] 10.1137/040608714
[DOI] http://dx.doi.org/10.1137/040608714 isVersionOf