ArticleJournal of mathematical biology2023
conditions for Turing and wave instabilities in reaction-diffusion systems.
Article in Journal of mathematical biology, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. An erratum has been issued. Cited by 6 papers.
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6 citing papers in PubMed.
- Cell-Size Confinement Drives Size-Dependent Scaling of Intracellular Reaction-Diffusion Waves for Robust Patterning.Small science · 2026Article
- Designing reaction-cross-diffusion systems with Turing and wave instabilities.Journal of mathematical biology · 2025Article
- Pattern Formation as a Resilience Mechanism in Cancer Immunotherapy.Bulletin of mathematical biology · 2025Article
- Analysis of the spatio-temporal dynamics of a Rho-GEF-H1-myosin activator-inhibitor reaction-diffusion system.Royal Society open science · 2025Article
- Route to Measure Exact Parameters of Bio-Nanostructures Self-Assembly.Biomolecules · 2024Article
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Corrections and comments
- Erratum issued
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2 authors.
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Abstract
Necessary and sufficient conditions are provided for a diffusion-driven instability of a stable equilibrium of a reaction-diffusion system with n components and diagonal diffusion matrix. These can be either Turing or wave instabilities. Known necessary and sufficient conditions are reproduced for there to exist diffusion rates that cause a Turing bifurcation of a stable homogeneous state in the absence of diffusion. The method of proof here though, which is based on study of dispersion relations in the contrasting limits in which the wavenumber tends to zero and to [Formula: see text], gives a constructive method for choosing diffusion constants. The results are illustrated on a 3-component FitzHugh-Nagumo-like model proposed to study excitable wavetrains, and for two different coupled Brusselator systems with 4-components.
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