Mind the gap: A solution to the robustness problem of Turing patterns through patterning mode isolation

Woolley, Thomas ORCID: https://orcid.org/0000-0001-6225-5365 2026. Mind the gap: A solution to the robustness problem of Turing patterns through patterning mode isolation. AppliedMath 6 (1) , 3.

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Abstract

Turing patterns, characterized by spatial self-organization in reaction-diffusion systems, exhibit sensitivity to initial conditions. This sensitivity, known as the robustness problem, results in different final patterns emerging even from small initial perturbations. In this paper, we introduce a mechanism of pattern mode isolation, where we investigate parameter regimes that promote the isolation of bifurcation branches, thereby delineating the conditions under which distinct pattern modes emerge and evolve independently. Pattern mode isolation can provide a means of enhancing the predictability of Turing pattern mode transitions and enhance the robustness and reproducibility of the patterning outputs.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	MDPI
ISSN:	2673-9909
Date of First Compliant Deposit:	27 November 2025
Date of Acceptance:	25 November 2025
Last Modified:	15 Jan 2026 15:32
URI:	https://orca.cardiff.ac.uk/id/eprint/182692

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