Pattern formation in a slowly flattening spherical cap: delayed bifurcation

Abstract This article describes a reduction of a non-autonomous Brusselator reaction–diffusion system of partial differential equations on a spherical cap with time-dependent curvature using the method of centre manifold reduction. Parameter values are chosen such that the change in curvature would...

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Bibliographic Details
Published inIMA journal of applied mathematics Vol. 85; no. 4; pp. 513 - 541
Main Authors Charette, Laurent, Macdonald, Colin B, Nagata, Wayne
Format Journal Article
LanguageEnglish
Published Oxford University Press 01.08.2020
Subjects
centre manifold reduction
delayed bifurcation
closest point method
Brusselator
pitchfork bifurcation
non-autonomous differential equation
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Summary:Abstract This article describes a reduction of a non-autonomous Brusselator reaction–diffusion system of partial differential equations on a spherical cap with time-dependent curvature using the method of centre manifold reduction. Parameter values are chosen such that the change in curvature would cross critical values which would change the stability of the patternless solution in the constant domain case. The evolving domain functions and quasi-patternless solutions are derived as well as a method to obtain this non-autonomous normal form. The coefficients of such a normal form are computed and the reduction solutions are compared to numerical solutions.
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/hxaa016