Eckhaus instability and homoclinic snaking.
Eckhaus instability and homoclinic snaking.
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艾克豪斯不稳定性和同宿蛇行。
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
I. Mercader
中科院分区：
文献类型：
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作者：
A. Bergeon;John P. Burke;Edgar Knobloch;I. Mercader
同宿蛇行是一个术语，用来描述一个时间无关的空间局域态的分支的来回振荡，在一个连续的，空间可逆的系统中，随着局域结构的长度增加，通过重复增加两侧的卷。这种行为在亚临界Swift-Hohenberg方程中最容易理解，但也存在于由水平梯度驱动的双扩散对流的亚临界状态中。在一个空间方向上无界的系统中，同宿蛇行无限地持续，因为局域结构增长到类似于无限范围的空间周期性状态。在有限域或具有有限空间周期的周期域中，该过程必须终止。在本文中，我们表明，蜿蜒的分支机构在一般情况下，一旦本地化状态的长度变得可比的域，并检查的因素，确定的终止点或点的位置，以及它们的关系的埃克豪斯不稳定性的空间周期性状态。
Homoclinic snaking is a term used to describe the back and forth oscillation of a branch of time-independent spatially localized states in a bistable, spatially reversible system as the localized structure grows in length by repeatedly adding rolls on either side. This behavior is simplest to understand within the subcritical Swift-Hohenberg equation, but is also present in the subcritical regime of doubly diffusive convection driven by horizontal gradients. In systems that are unbounded in one spatial direction homoclinic snaking continues indefinitely as the localized structure grows to resemble a spatially periodic state of infinite extent. In finite domains or in periodic domains with finite spatial period the process must terminate. In this paper we show that the snaking branches in general turn over once the length of the localized state becomes comparable to the domain, and examine the factors that determine the location of the termination point or points, and their relation to the Eckhaus instability of the spatially periodic state.