Houghton S M, Knobloch E
School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Aug;80(2 Pt 2):026210. doi: 10.1103/PhysRevE.80.026210. Epub 2009 Aug 20.
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. On the real line this process continues forever. In finite domains snaking terminates once the domain is filled but the details of how this occurs depend critically on the choice of boundary conditions. With periodic boundary conditions the snaking branches terminate on a branch of spatially periodic states. However, with non-Neumann boundary conditions they turn continuously into a large amplitude filling state that replaces the periodic state. This behavior, shown here in detail for the Swift-Hohenberg equation, explains the phenomenon of "snaking without bistability," recently observed in simulations of binary fluid convection by Mercader et al. Phys. Rev. E 80, 025201 (2009).
同宿蛇行是一个术语，用于描述在双稳空间可逆系统中，与时间无关的空间局域态分支的来回振荡，这种振荡是随着局域结构通过在两侧反复添加滚动而长度增加时出现的。在实直线上，这个过程会永远持续下去。在有限域中，一旦域被填满，蛇行就会终止，但这一过程发生的细节关键取决于边界条件的选择。对于周期边界条件，蛇行分支终止于空间周期态分支。然而，对于非诺伊曼边界条件，它们会连续转变为一个取代周期态的大幅填充态。这里针对Swift-Hohenberg方程详细展示的这种行为，解释了最近在Mercader等人的二元流体对流模拟中观察到的“无双稳蛇行”现象[《物理评论E》80, 025201 (2009)]。
