论文标题
从图灵分叉出现的模式的二面环
Dihedral rings of patterns emerging from a Turing bifurcation
论文作者
论文摘要
当模式受到弱或半突变的相互作用时，将模式的集体组织成类似环形的配置。但是，当模式强烈相互作用时，在数值或分析上几乎没有知道它们的形成。我们证明，近似强烈的相互作用模式可以在各种环状二面构型中出现，这是从通用的两分量反应 - 扩散系统中图灵不稳定性附近的静止而分叉的。所使用的方法是建设性的，并为数值延续方法提供了准确的初始条件，以遵循参数空间中的这些类似环形模式。我们的分析得到了数字研究的补充，这些研究说明了我们的发现。
Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is known numerically or analytically about their formation when the patterns are strongly interacting. We prove that approximate strongly interacting patterns can emerge in various ring-like dihedral configurations, bifurcating from quiescence near a Turing instability in generic two-component reaction-diffusion systems. The methods used are constructive and provide accurate initial conditions for numerical continuation methods to path-follow these ring-like patterns in parameter space. Our analysis is complemented by numerical investigations that illustrate our findings.
