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Dynamics of traveling pulses in heterogeneous media

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Title: Dynamics of traveling pulses in heterogeneous media
Authors: Nishiura, Yasumasa Browse this author →KAKEN DB
Teramoto, Takashi Browse this author
Yuan, Xiaohui Browse this author
Ueda, Kei-Ichi Browse this author
Issue Date: Sep-2007
Publisher: American Institute of Physics
Journal Title: Chaos : An Interdisciplinary Journal of Nonlinear Science
Volume: 17
Issue: 3
Start Page: 037104
Publisher DOI: 10.1063/1.2778553
PMID: 17903011
Abstract: One of the fundamental issues of pulse dynamics in dissipative systems is clarifying how the heterogeneity in the media influences the propagating manner. Heterogeneity is the most important and ubiquitous type of external perturbation. We focus on a class of one-dimensional traveling pulses, the associated parameters of which are close to drift and/or saddle-node bifurcations. The advantage in studying the dynamics in such a class is twofold: First, it gives us a perfect microcosm for the variety of outputs in a general setting when pulses encounter heterogeneities. Second, it allows us to reduce the original partial differential equation dynamics to a tractable finite-dimensional system. Such pulses are sensitive when they run into heterogeneities and show rich responses such as annihilation, pinning, splitting, rebound, as well as penetration. The reduced ordinary differential equations (ODEs) explain all these dynamics and the underlying bifurcational structure controlling the transitions among different dynamic regimes. It turns out that there are hidden ordered patterns associated with the critical points of ODEs that play a pivotal role in understanding the responses of the pulse; in fact, the depinning of pulses can be explained in terms of global bifurcations among those critical points. We focus mainly on a bump and periodic types of heterogeneity, however our approach is also applicable to general cases. It should be noted that there appears to be spatio-temporal chaos for a periodic type of heterogeneity when its period becomes comparable with the size of the pulse. ©2007 American Institute of Physics
Rights: Copyright 2007 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
Type: article
Appears in Collections:電子科学研究所 (Research Institute for Electronic Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 西浦 廉政

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