Stability of bifurcating solutions of the Gierer-Meinhardt system

DOI10.2748/tmj/1178229841zbMath0414.35043OpenAlexW2093193384MaRDI QIDQ599280

Izumi Takagi

Publication date: 1979

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178229841

zbMATH Keywords

bifurcationstationary solutionsactivator-inhibitor modelnonlinear diffusionhomogeneous Neumann boundary conditionbiological pattern formation

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Bifurcations in context of PDEs (35B32) Miscellaneous topics in partial differential equations (35R99) General biology and biomathematics (92B05)

Related Items (9)

Spatial resonance and Turing-Hopf bifurcations in the Gierer-Meinhardt model ⋮ Point-condensation for a reaction-diffusion system ⋮ Bifurcation Analysis of a Diffusive Activator–Inhibitor Model in Vascular Mesenchymal Cells ⋮ Global existence and finite time blow-up of solutions of a Gierer-Meinhardt system ⋮ Supercritical Hopf bifurcation and Turing patterns for an activator and inhibitor model with different sources ⋮ A priori estimates for stationary solutions of an activator-inhibitor model due to Gierer and Meinhardt ⋮ Bifurcation analysis of the Gierer–Meinhardt system with a saturation in the activator production ⋮ Remarks on pattern formation in a model for hair follicle spacing ⋮ Spatial inhomogenity due to Turing bifurcation in a system of Gierer-Meinhardt type

Cites Work

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• Dynamics of patterns and interfaces in some reaction-diffusion systems from chemical and biological viewpoints.
• Stability and semilinear evolution equations in Hilbert space
• A bifurcation analysis of pattern formation in a diffusion governed morphogenetic field
• Bifurcation, perturbation of simple eigenvalues, and linearized stability
• Bifurcation from simple eigenvalues
• The chemical basis of morphogenesis

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