Existence and stability analysis of spiky solutions for the Gierer-Meinhardt system with large reaction rates

DOI10.1016/j.physd.2009.05.009zbMath1179.37120OpenAlexW2070596673MaRDI QIDQ843018

Matthias Winter, Theodore Kolokolnikov, Wei, Juncheng

Publication date: 28 September 2009

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2009.05.009

zbMATH Keywords

stabilitysingular perturbationsTuring instabilitymultiple-peaked solutions

Mathematics Subject Classification ID

General biostatistics (92B15) Reaction-diffusion equations (35K57) Dynamical systems in biology (37N25)

Related Items

Bifurcation and Turing patterns of reaction-diffusion activator-inhibitor model ⋮ Slow localized patterns in singularly perturbed two-component reaction–diffusion equations ⋮ Existence, Stability, and Dynamics of Ring and Near-Ring Solutions to the Saturated Gierer--Meinhardt Model in the Semistrong Regime ⋮ Codimension-Two Bifurcation Analysis on a Discrete Gierer–Meinhardt System ⋮ Stabilizing a homoclinic stripe ⋮ The existence and stability of spikes in the one-dimensional Keller-Segel model with logistic growth ⋮ Tracking pattern evolution through extended center manifold reduction and singular perturbations

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• Hopf bifurcation of spike solutions for the shadow GiererMeinhardt model
• The stability of spike solutions to the one-dimensional Gierer-Meinhardt model

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