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arXiv · 2210.13122

Dihedral rings of patterns emerging from a Turing bifurcation

Dan J. Hill·Jason J. Bramburger·David J. B. Lloyd
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Abstract

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.

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Dan J. Hill, Jason J. Bramburger, David J. B. Lloyd. 2022-10-24. Dihedral rings of patterns emerging from a Turing bifurcation. https://doi.org/10.1088/1361-6544%2Fad2221

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