Homoclinic Stripe Patterns
Homoclinic Stripe Patterns
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同宿条纹图案
DOI：
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发表时间：
2002
影响因子：
2.1
通讯作者：
H. V. D. Ploeg
中科院分区：
文献类型：
--
作者：
A. Doelman;H. V. D. Ploeg
本文研究二维广义Gierer-Meinhardt方程的同宿条纹，将其解释为一类奇摄动的单稳态反应扩散方程的典型代表。条纹图案的结构本质上是一维的，因此，我们可以利用文献中的结果来确定同宿图案的存在性。然而，我们将这些结果推广到参数空间中的极大区域，并建立了该区域上形成新的上界的分支的存在性。在这种分叉之后，Gierer-Meinhardt方程分别在一维、二维中呈现出自复制脉冲和条纹(S)。自我复制过程的结构与格雷-斯科特方程中的结构非常相似。通过对相关线性本征值问题的Evans函数分析，我们研究了同宿条纹图的稳定性。我们扩展了最近开发的.
In this paper, we study homoclinic stripe patterns in the two-dimensional generalized Gierer--Meinhardt equation, where we interpret this equation as a prototypical representative of a class of singularly perturbed monostable reaction-diffusion equations. The structure of a stripe pattern is essentially one-dimensional; therefore, we can use results from the literature to establish the existence of the homoclinic patterns. However, we extend these results to a maximal domain in the parameter space and establish the existence of a bifurcation that forms a new upper bound on this domain. Beyond this bifurcation, the Gierer--Meinhardt equation exhibits self-replicating pulse, respectively, stripe patterns in one, respectively, two dimension(s). The structure of the self-replication process is very similar to that in the Gray--Scott equation. We investigate the stability of the homoclinic stripe patterns by an Evans function analysis of the associated linear eigenvalue problem. We extend the recently develope...