Dynamics of traveling pulses in heterogeneous media.
Dynamics of traveling pulses in heterogeneous media.
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DOI：
10.1063/1.2778553
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发表时间：
2007-09
期刊：
影响因子：
2.9
通讯作者：
Y. Nishiura;T. Teramoto;Xiaohui Yuan;Kei-Ichi Ueda
中科院分区：
文献类型：
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作者：
Y. Nishiura;T. Teramoto;Xiaohui Yuan;Kei-Ichi Ueda
耗散系统中脉冲动力学的基本问题之一是阐明介质中的非均匀性如何影响脉冲的传播方式。异质性是最重要和最普遍的外部扰动类型。我们专注于一类一维行波脉冲，其相关参数接近漂移和/或鞍结分岔。在这样一个类中研究动力学的优点是双重的：首先，它为我们提供了一个完美的微观世界，当脉冲遇到异质性时，在一般设置中的各种输出。其次，它使我们能够减少原来的偏微分方程动力学一个易于处理的有限维系统。这种脉冲在非均匀性中表现出很高的灵敏度，表现出丰富的响应，如湮灭、钉扎、分裂、反弹和穿透等。简化的常微分方程（ODE）解释了所有这些动态和控制不同动态机制之间的转换的基本分叉结构。事实证明，存在与常微分方程的临界点相关的隐藏有序模式，这些临界点在理解脉冲的响应方面起着关键作用;事实上，脉冲的脱钉可以用这些临界点之间的全局分叉来解释。我们主要关注凹凸和周期性类型的异质性，但我们的方法也适用于一般情况。应该指出的是，似乎有时空混沌的周期性类型的异质性时，其周期变得与脉冲的大小相媲美。
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.