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Boundary conditions cause different generic bifurcation structures in Turing systems

Woolley, Thomas ORCID: https://orcid.org/0000-0001-6225-5365 2022. Boundary conditions cause different generic bifurcation structures in Turing systems. Bulletin of Mathematical Biology 84 (9) , 101.

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Abstract

Turing’s theory of morphogenesis is a generic mechanism to produce spatial patterning from near homogeneity. Although widely studied, we are still able to generate new results by returning to common dogmas. One such widely reported belief is that the Turing bifurcation occurs through a pitchfork bifurcation, which is true under zero-flux boundary conditions. However, under fixed boundary conditions, the Turing bifurcation becomes generically transcritical. We derive these algebraic results through weakly nonlinear analysis and apply them to the Schnakenberg kinetics. We observe that the combination of kinetics and boundary conditions produce their own uncommon boundary complexities that we explore numerically. Overall, this work demonstrates that it is not enough to only consider parameter perturbations in a sensitivity analysis of a specific application. Variations in boundary conditions should also be considered.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Additional Information: This article is licensed under a Creative Commons Attribution 4.0 International License
Publisher: Springer
ISSN: 0092-8240
Date of First Compliant Deposit: 17 July 2022
Date of Acceptance: 15 July 2022
Last Modified: 10 Nov 2022 19:40
URI: https://orca.cardiff.ac.uk/id/eprint/151340

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