The dynamics of a kinetic activator -- inhibitor system

DOI10.1016/j.jde.2006.03.011zbMath1108.34044OpenAlexW2007171537MaRDI QIDQ852684

Kanako Suzuki, Izumi Takagi, Wei-Ming Ni

Publication date: 15 November 2006

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2006.03.011

zbMATH Keywords

reaction-diffusion systemkinetic system

Mathematics Subject Classification ID

Classical flows, reactions, etc. in chemistry (92E20) Qualitative investigation and simulation of ordinary differential equation models (34C60) Qualitative theory for ordinary differential equations (34Cxx)

Related Items (16)

On the global existence and finite time blow-up of shadow systems ⋮ Finite-time blowup of solutions to some activator-inhibitor systems ⋮ Global existence and finite time blow-up of solutions of a Gierer-Meinhardt system ⋮ Finite-time blow-up and blow-up rates for the Gierer–Meinhardt system ⋮ On a class of singular Gierer-Meinhardt systems arising in morphogenesis ⋮ Steady-state solutions for Gierer-Meinhardt type systems with Dirichlet boundary condition ⋮ Dynamical spike solutions in a nonlocal model of pattern formation ⋮ The dynamics of the stochastic shadow Gierer-Meinhardt system ⋮ Steady state solutions for the Gierer-Meinhardt system in the whole space ⋮ Supercritical Hopf bifurcation and Turing patterns for an activator and inhibitor model with different sources ⋮ On global existence for the Gierer-Meinhardt system ⋮ Behaviors of solutions for a singular prey-predator model and its shadow system ⋮ Existence, nonexistence and uniqueness of positive stationary solutions of a singular Gierer-Meinhardt system ⋮ MULTIPLE BIFURCATION ANALYSIS AND SPATIOTEMPORAL PATTERNS IN A 1-D GIERER–MEINHARDT MODEL OF MORPHOGENESIS ⋮ Dynamics of shadow system of a singular Gierer-Meinhardt system on an evolving domain ⋮ Remarks on pattern formation in a model for hair follicle spacing

Cites Work

• Unnamed Item
• Unnamed Item
• Global solutions of reaction-diffusion systems
• Global existence of solutions of an activator-inhibitor system
• Boundedness and blow up for the general activator-inhibitor model
• Reaction-diffusion systems in the Gierer-Meinhardt theory of biological pattern formation
• The chemical basis of morphogenesis
• On the Role of Basic Production Terms in an Activator-Inhibitor System Modeling Biological Pattern Formation

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