Transition from polar to duplicate patterns

DOI10.1007/BF00276025zbMath0433.92002WikidataQ52298472 ScholiaQ52298472MaRDI QIDQ1139512

Jacques Hiernaux, Thomas Erneux

Publication date: 1980

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

zbMATH Keywords

pattern formationnonlinear reaction-diffusion systemsbifurcation diagram of small amplitude solutionsexistence of symmetric nonuniform solutionsstable symmetric solution

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Bifurcations in context of PDEs (35B32) General biology and biomathematics (92B05) Physiological, cellular and medical topics (92Cxx)

Related Items

A non-linear analysis for spatial structure in a reaction-diffusion model

Cites Work

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• Models for cell differentiation and generation of polarity in diffusion- governed morphogenetic fields
• Bifurcation analysis of nonlinear reaction-diffusion equations. II: Steady state solutions and comparison with numerical simulations
• Bifurcation analysis of nonlinear reaction diffusion equations I. Evolution equations and the steady state solutions
• On modelling pattern formation by activator-inhibitor systems
• Dissipative Structures, Catastrophes, and Pattern Formation: A Bifurcation Analysis
• Secondary Bifurcation in Nonlinear Diffusion Reaction Equations
• A Model Biochemical Reaction Exhibiting Secondary Bifurcation
• Singular Perturbations of Bifurcations
• On the Validity of the Two-Timing Method for Large Times
• Activators and Inhibitors in Pattern Formation