Localized patterns and semi-strong interaction, a unifying framework for reaction–diffusion systems

DOI10.1093/imamat/hxab036zbMath1480.92092OpenAlexW3194959756MaRDI QIDQ5020376

Fahad Al Saadi, Nicolas Verschueren, Alan R. Champneys

Publication date: 5 January 2022

Published in: IMA Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1093/imamat/hxab036

zbMATH Keywords

reaction-diffusionTuring instabilitySchnakenberghomoclinic snakinglocalized patternsBrusselator

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Bifurcations in context of PDEs (35B32)

Related Items (8)

Spikes and localised patterns for a novel Schnakenberg model in the semi-strong interaction regime ⋮ Demonstration of unique problems from soliton solutions to nonlinear Selkov-Schnakenberg system ⋮ Analysing transitions from a Turing instability to large periodic patterns in a reaction-diffusion system ⋮ Degenerate Turing Bifurcation and the Birth of Localized Patterns in Activator-Inhibitor Systems ⋮ Spatial heterogeneity localizes Turing patterns in reaction-cross-diffusion systems ⋮ General conditions for Turing and wave instabilities in reaction-diffusion systems ⋮ Localised spatial structures in the Thomas model ⋮ Traveling pulses with oscillatory tails, figure-eight-like stack of isolas, and dynamics in heterogeneous media

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