Bifurcation of spike equilibria in the near-shadow Gierer-Meinhardt model

DOI10.3934/dcdsb.2004.4.1033zbMath1063.35084OpenAlexW2036608022MaRDI QIDQ1884256

Theodore Kolokolnikov, Michael J. Ward

Publication date: 27 October 2004

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/4fa6ffa8ed0a750bb4d129d8ab07ee116d706b60

zbMATH Keywords

Green's functionpattern formationpitchfork bifurcation

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Green's functions for ordinary differential equations (34B27) Developmental biology, pattern formation (92C15) Bifurcations in context of PDEs (35B32)

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The stability of steady-state hot-spot patterns for a reaction-diffusion model of urban crime ⋮ Stationary multiple spots for reaction-diffusion systems ⋮ The Gierer-Meinhardt system on a compact two-dimensional Riemannian manifold: Interaction of Gaussian curvature and Green's function ⋮ Isolating patterns in open reaction-diffusion systems ⋮ Stable spike clusters on a compact two-dimensional Riemannian manifold ⋮ Localized outbreaks in an S-I-R model with diffusion

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