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Dihedral rings of patterns emerging from a Turing bifurcation
Nonlinearity ( IF 1.7 ) Pub Date : 2024-02-09 , DOI: 10.1088/1361-6544/ad2221 Dan J Hill , Jason J Bramburger , David J B Lloyd
Nonlinearity ( IF 1.7 ) Pub Date : 2024-02-09 , DOI: 10.1088/1361-6544/ad2221 Dan J Hill , Jason J Bramburger , David J B Lloyd
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.
更新日期：2024-02-09
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