ArticleJournal of mathematical biology2021
Turing conditions for pattern forming systems on evolving manifolds.
Article in Journal of mathematical biology, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 14 papers.
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14 citing papers in PubMed.
- Cell-Size Confinement Drives Size-Dependent Scaling of Intracellular Reaction-Diffusion Waves for Robust Patterning.Small science · 2026Article
- A computational framework to study EGFR signaling distribution in egg chambers during dynamic interactions between soma and germline.PLoS computational biology · 2025Article
- Characterizing symmetry transitions in systems with dynamic morphology.Mathematical biosciences · 2025Article
- Periodic pattern formation during embryonic development.Biochemical Society transactions · 2024Review
- Fluctuations in auxin levels depend upon synchronicity of cell divisions in a one-dimensional model of auxin transport.PLoS computational biology · 2023Article
- Concentration-Dependent Domain Evolution in Reaction-Diffusion Systems.Bulletin of mathematical biology · 2023Article
- Boundary Conditions Cause Different Generic Bifurcation Structures in Turing Systems.Bulletin of mathematical biology · 2022Article
- Turing pattern design principles and their robustness.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2021Review
- Modern perspectives on near-equilibrium analysis of Turing systems.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2021Review
- Reaction-diffusion models for morphological patterning of hESCs.Journal of mathematical biology · 2021Article
- Isolating Patterns in Open Reaction-Diffusion Systems.Bulletin of mathematical biology · 2021Article
- Influence of survival, promotion, and growth on pattern formation in zebrafish skin.Scientific reports · 2021Article
- Bespoke Turing Systems.Bulletin of mathematical biology · 2021Article
- Turing Patterning in Stratified Domains.Bulletin of mathematical biology · 2020Article
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3 authors.
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Abstract
The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental chemistry. Analyzing such instabilities is complicated, as there is a strong dependence of any spatially homogeneous base states on time, and the resulting structure of the linearized perturbations used to determine the onset of instability is inherently non-autonomous. We obtain general conditions for the onset and structure of diffusion driven instabilities in reaction-diffusion systems on domains which evolve in time, in terms of the time-evolution of the Laplace-Beltrami spectrum for the domain and functions which specify the domain evolution. Our results give sufficient conditions for diffusive instabilities phrased in terms of differential inequalities which are both versatile and straightforward to implement, despite the generality of the studied problem. These conditions generalize a large number of results known in the literature, such as the algebraic inequalities commonly used as a sufficient criterion for the Turing instability on static domains, and approximate asymptotic results valid for specific types of growth, or specific domains. We demonstrate our general Turing conditions on a variety of domains with different evolution laws, and in particular show how insight can be gained even when the domain changes rapidly in time, or when the homogeneous state is oscillatory, such as in the case of Turing-Hopf instabilities. Extensions to higher-order spatial systems are also included as a way of demonstrating the generality of the approach.
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