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
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Creator |
Nishiura Y
Ueyama Daishin
Yanagita T
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Source Title |
SIAM Journal on Applied Dynamical Systems
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Volume | 4 |
Issue | 3 |
Start Page | 733 |
End Page | 754 |
Keywords |
Bifurcation theory
Chaos
Dissipative systems
Lattice differential equation
LDE
Localized pulse
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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.
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NDC |
Mathematics [ 410 ]
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Language |
eng
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Resource Type | journal article |
Publisher |
Society for Industrial and Applied Mathematics
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Date of Issued | 2005 |
Rights |
Copyright (c) 2005 Society for Industrial and Applied Mathematics
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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
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