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Reaction-diffusion systems in the Gierer-Meinhardt theory of biological pattern formation

https://doi.org/10.1007/bf03167754
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/978-3-642-66282-9openalex-snapshot
Perturbation Theory for Linear Operators
inferredcites →https://doi.org/10.1007/bf00276349openalex-snapshot
A bifurcation analysis of pattern formation in a diffusion governed morphogenetic field
inferredcites →https://doi.org/10.1007/bf00289234openalex-snapshot
A theory of biological pattern formation
inferredcites →https://doi.org/10.1007/bfb0089647openalex-snapshot
Geometric Theory of Semilinear Parabolic Equations
inferredcites →https://doi.org/10.1007/bfb0099278openalex-snapshot
Global Solutions of Reaction-Diffusion Systems
inferredcites →https://doi.org/10.1016/0022-0396(86)90119-1openalex-snapshot
Point-condensation for a reaction-diffusion system
inferredcites →https://doi.org/10.1090/s0002-9947-1986-0849484-2openalex-snapshot
On the Neumann Problem for Some Semilinear Elliptic Equations and Systems of Activator-Inhibitor Type
inferredcites →https://doi.org/10.14492/hokmj/1470081012openalex-snapshot
On the global existence and asymptotic behavior of solutions of reaction-diffusion equations
inferredcites →https://doi.org/10.2748/tmj/1178229312openalex-snapshot
A priori estimates for stationary solutions of an activator-inhibitor model due to Gierer and Meinhardt

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1002/mma.3502openalex-snapshot
Large-time behaviour and blow up of solutions for Gierer-Meinhardt systems
inferred← citeshttps://doi.org/10.1007/978-3-319-11322-7_8openalex-snapshot
Reaction-Diffusion-ODE Models of Pattern Formation
inferred← citeshttps://doi.org/10.1007/978-3-319-67944-0_5openalex-snapshot
Gierer–Meinhardt System
inferred← citeshttps://doi.org/10.1007/978-3-7643-8442-5_6openalex-snapshot
Nonlocal Problems
inferred← citeshttps://doi.org/10.1007/s00033-011-0149-9openalex-snapshot
A remark on global existence of solutions of shadow systems
inferred← citeshttps://doi.org/10.1007/s00245-022-09835-6openalex-snapshot
The Stochastic Gierer–Meinhardt System
inferred← citeshttps://doi.org/10.1007/s00332-020-09664-3openalex-snapshot
Dynamics of Shadow System of a Singular Gierer–Meinhardt System on an Evolving Domain
inferred← citeshttps://doi.org/10.1007/s41808-018-0028-zopenalex-snapshot
Dynamical system for animal coat pattern model
inferred← citeshttps://doi.org/10.1016/j.aml.2020.106348openalex-snapshot
Some results on the Gierer–Meinhardt model with critical exponent p−1=r
inferred← citeshttps://doi.org/10.1016/j.jde.2005.04.008openalex-snapshot
Upper semicontinuity of the global attractor for the Gierer–Meinhardt model
inferred← citeshttps://doi.org/10.1016/j.jde.2006.03.011openalex-snapshot
The dynamics of a kinetic activator–inhibitor system
inferred← citeshttps://doi.org/10.1016/j.jde.2009.04.009openalex-snapshot
On the global existence and finite time blow-up of shadow systems
inferred← citeshttps://doi.org/10.1016/j.jde.2016.09.040openalex-snapshot
Global existence and finite time blow-up of solutions of a Gierer–Meinhardt system
inferred← citeshttps://doi.org/10.1016/j.jde.2025.113559openalex-snapshot
The Gierer-Meinhardt system in the entire space with non-local proliferation rates
inferred← citeshttps://doi.org/10.1016/j.jocs.2025.102651openalex-snapshot
A computational approach for solving the Gierer-Meinhardt (G-M) model in the context of biological pattern formation
inferred← citeshttps://doi.org/10.1016/j.na.2020.111785openalex-snapshot
Global existence and blowup solutions for the Gierer–Meinhardt system
inferred← citeshttps://doi.org/10.1088/1361-6544/aa64b2openalex-snapshot
On the dynamics of a non-local parabolic equation arising from the Gierer–Meinhardt system
inferred← citeshttps://doi.org/10.1155/2013/939405openalex-snapshot
Global Solutions for an -Component System of Activator-Inhibitor Type
inferred← citeshttps://doi.org/10.11948/20190306openalex-snapshot
GLOBAL ANALYSIS OF THE SHADOW GIERER-MEINHARDT SYSTEM WITH GENERAL LINEAR BOUNDARY CONDITIONS IN A RANDOM ENVIRONMENT
inferred← citeshttps://doi.org/10.14943/49023openalex-snapshot
Proceeding of the 33rd Sapporo Symposium on Partial Differential Equations
inferred← citeshttps://doi.org/10.1512/iumj.2007.56.2982openalex-snapshot
A priori estimates of stationary solutions of an activator-inhibitor system
inferred← citeshttps://doi.org/10.1619/fesi.54.237openalex-snapshot
On the Role of Basic Production Terms in an Activator-Inhibitor System Modeling Biological Pattern Formation
inferred← citeshttps://doi.org/10.2969/aspm/04720689openalex-snapshot
Determination of the limit sets of trajectories of the Gierer-Meinhardt system without diffusion
inferred← citeshttps://doi.org/10.3934/cpaa.2022013openalex-snapshot
Analysis and asymptotic reduction of a bulk-surface reaction-diffusion model of Gierer-Meinhardt type
inferred← citeshttps://doi.org/10.3934/dcds.2013.33.2885openalex-snapshot
Global-in-time behavior of the solution to a Gierer-Meinhardt system
inferred← citeshttps://doi.org/10.3934/dcds.2015.35.583openalex-snapshot
On global existence for the Gierer-Meinhardt system
inferred← citeshttps://doi.org/10.3934/dcds.2016016openalex-snapshot
Finite-time blowup of solutions to some activator-inhibitor systems
inferred← citeshttps://doi.org/10.3934/dcdsb.2015.20.1555openalex-snapshot
Remarks on pattern formation in a model for hair follicle spacing
inferred← citeshttps://doi.org/10.3934/dcdsb.2020357openalex-snapshot
The spatially heterogeneous diffusive rabies model and its shadow system
inferred← citeshttps://doi.org/10.4236/am.2017.86067openalex-snapshot
Global Existence of Solutions of the Gierer-Meinhardt System with Mixed Boundary Conditions
inferred← citeshttps://doi.org/10.48550/arxiv.1007.4029openalex-snapshot
Global existence of solutions for Gierer-Meinhardt system with three equations
inferred← citeshttps://doi.org/10.48550/arxiv.2010.04426openalex-snapshot
Analysis and numerical treatment of bulk-surface reaction-diffusion models of Gierer-Meinhardt type
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