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Dynamics of traveling pulses in heterogeneous media

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タイトル: Dynamics of traveling pulses in heterogeneous media
著者: Nishiura, Yasumasa 著作を一覧する
Teramoto, Takashi 著作を一覧する
Yuan, Xiaohui 著作を一覧する
Ueda, Kei-Ichi 著作を一覧する
発行日: 2007年 9月
出版者: American Institute of Physics
誌名: Chaos : An Interdisciplinary Journal of Nonlinear Science
巻: 17
号: 3
開始ページ: 037104
出版社 DOI: 10.1063/1.2778553
抄録: 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.
関連URI: http://chaos.aip.org/chaos/
資料タイプ: article
URI: http://hdl.handle.net/2115/30298
出現コレクション:雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

提供者: 西浦 廉政

 

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