PATTERN-FORMATION IN NONGRADIENT REACTION-DIFFUSION SYSTEMS - THE EFFECTS OF FRONT BIFURCATIONS
PATTERN-FORMATION IN NONGRADIENT REACTION-DIFFUSION SYSTEMS - THE EFFECTS OF FRONT BIFURCATIONS
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DOI：
10.1088/0951-7715/7/3/006
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发表时间：
1994-05-01
期刊：
影响因子：
1.7
通讯作者：
MERON, E
中科院分区：
文献类型：
--
作者：
HAGBERG, A;MERON, E
反应扩散系统中的域模式通常包含两个空间尺度；一个长尺度是由典型的域大小决定的，一个短尺度是由分隔不同域的前端结构决定的。这种模式在双稳态和可激系统中自然发展，但也可能远远超出Hopf和Turing分岔。区域模式的全局行为强烈依赖于锋面的内部结构。本文研究了一类广泛的反应扩散系统中可能出现的对称破缺锋分岔，以及它对模式形成和模式动力学的影响。我们扩展了前人关于这类锋面分岔的研究，并澄清了它们之间的关系。我们表明，超越分岔点的前沿多样性的出现允许形成持久的模式，而不是短暂的模式。在不同的参数状态下，我们发现前分岔概述了从振荡（或呼吸）模式到行进模式的过渡。在边界附近，我们发现分叉以外的锋面可以反射，而分叉以下的锋面要么与边界绑定，要么消失。
Domain patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally develop in bistable and excitable systems, but may also appear far beyond Hopf and Turing bifurcations. The global behaviour of domain patterns strongly depends on the fronts' inner structures. In this paper we study a symmetry breaking front bifurcation expected to occur in a wide class of reaction-diffusion systems, and the effects it has on pattern formation and pattern dynamics. We extend previous works on this type of front bifurcation and clarify the relations among them. We show that the appearance of front multiplicity beyond the bifurcation point allows the formation of persistent patterns rather than transient ones. In a different parameter regime, we find that the front bifurcation outlines a transition from oscillating (or breathing) patterns to travelling ones. Near a boundary we find that fronts beyond the bifurcation can reflect, while those below it either bind to the boundary or disappear.