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Updated: Aug 12, 2025

Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
conditions for Turing and wave instabilities in reaction-diffusion systems
Edgardo Villar-Sepúlveda1, Alan R Champneys2
1Engineering Mathematics, University of Bristol, Ada Lovelace Building, Tankard's Cl, University Walk, Bristol, Somerset, BS8 1TW, UK. edgardo.villar-sepulveda@bristol.ac.uk.
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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