このエントリーをはてなブックマークに追加
ID 14679
file
creator
Nishiura, Y
Ueyama, Daishin
Yanagita, T
subject
Bifurcation theory
Chaos
Dissipative systems
Lattice differential equation
LDE
Localized pulse
NDC
Mathematics
description
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.
journal title
SIAM Journal on Applied Dynamical Systems
volume
Volume 4
issue
Issue 3
start page
733
end page
754
date of issued
2005
publisher
Society for Industrial and Applied Mathematics
issn
1536-0040
publisher doi
language
eng
nii type
Journal Article
HU type
Journal Articles
DCMI type
text
format
application/pdf
text version
author
rights
Copyright (c) 2005 Society for Industrial and Applied Mathematics
relation is version of URL
http://dx.doi.org/10.1137/040608714
department
Graduate School of Science