Stable asymmetric spike equilibria for the Gierer–Meinhardt model with a precursor field

DOI10.1093/imamat/hxaa023zbMath1460.35014arXiv2002.01608OpenAlexW3005254274MaRDI QIDQ5855287

Michael J. Ward, Frédéric Paquin-Lefebvre, Theodore Kolokolnikov

Publication date: 18 March 2021

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

Full work available at URL: https://arxiv.org/abs/2002.01608

zbMATH Keywords

global bifurcation diagramanalytical-numerical approachlocalized peaks in the activatorsupercritical symmetry-breaking bifurcation

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Bifurcations in context of PDEs (35B32) Semilinear parabolic equations (35K58) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (9)

Stability of Spike Solutions to the Fractional Gierer-Meinhardt System in a One-Dimensional Domain ⋮ Turing–Hopf Bifurcation in Diffusive Gierer–Meinhardt Model ⋮ Spiky patterns for the Schnakenberg model with advection term on \(Y\)-shaped metric graph ⋮ Multi-peak solutions for the Schnakenberg model with heterogeneity on star shaped graphs ⋮ Multi-spike patterns for the Gierer-Meinhardt model with heterogeneity on \(Y\)-shaped metric graph ⋮ Concentration phenomena on \(Y\)-shaped metric graph for the Gierer-Meinhardt model with heterogeneity ⋮ Competition instabilities of spike patterns for the 1D Gierer–Meinhardt and Schnakenberg models are subcritical ⋮ Multi-spike patterns in the Gierer-Meinhardt system with a nonzero activator boundary flux ⋮ A ring of spikes in a Schnakenberg model

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