Pattern formation in morphogenesis. Analytical treatment of the Gierer- Meinhardt model on a sphere

DOI10.1007/BF01832840zbMath0497.92002OpenAlexW2922316870WikidataQ70455106 ScholiaQ70455106MaRDI QIDQ1171011

Christoph Berding, Hermann Haken

Publication date: 1982

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01832840

zbMATH Keywords

pattern formationreaction-diffusion equationsmorphogenesisGierer-Meinhardt model on sphere

Mathematics Subject Classification ID

Perturbations in context of PDEs (35B20) Initial value problems for linear higher-order PDEs (35G10) General biology and biomathematics (92B05) Higher-order parabolic equations (35K25) Physiological, cellular and medical topics (92Cxx)

Related Items (8)

Analysis and asymptotic reduction of a bulk-surface reaction-diffusion model of Gierer-Meinhardt type ⋮ Limit cycles in morphogenesis ⋮ Point-condensation for a reaction-diffusion system ⋮ Hopf bifurcation and multiple limit cycles in bio-chemical reaction of the morphogenesis process ⋮ Wavelength selection mechanism in the Gierer-Meinhardt model ⋮ Regulation of differentiation in a population of cells interacting through a common pool ⋮ Mathematical analysis of an activation-inhibition system in a discrete field ⋮ Pattern formation and morphogenesis: A reaction-diffusion model

Cites Work

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• Analytical treatment of pattern formation in the Gierer-Meinhardt model of morphogenesis
• Synergetics. An introduction. Nonequilibrium phase transitions and self- organization in physics, chemistry and biology. 2nd enl. ed
• Topics in stability and bifurcation theory
• Branching from Closely Spaced Eigenvalues with Application to a Model Biochemical Reaction
• Bifurcation of Localized Disturbances in a Model Biochemical Reaction
• A Model Biochemical Reaction Exhibiting Secondary Bifurcation
• Activators and Inhibitors in Pattern Formation
• The chemical basis of morphogenesis
• Perturbation Theory of Nonlinear Boundary-Value Problems
• A simple nonlinear dynamic stability problem

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