On the public citation graph

Analytical treatment of pattern formation in the Gierer-Meinhardt model of morphogenesis

0 signed · 86 inferred · view as graph

Inferred edges come from two machine sources: sweeps of open repository metadata (mostly SSRN and Zenodo), and a bulk OpenAlex citation snapshot. Every row below is labelled with the one it came from. Neither is a complete citation index — absence here is not evidence of absence.

Is this your work? Sign in with ORCID and put your name on the claims that are yours.
Claim with ORCID
Reference health. See whether every reference in this work resolves to a known work and none has been retracted — and get a dated CiteStamped badge you can embed.
See reference health

What this work says

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

inferredcites →https://doi.org/10.1007/978-1-4612-6374-6openalex-snapshot
The Hopf Bifurcation and Its Applications
inferredcites →https://doi.org/10.1007/978-3-642-66784-8_19openalex-snapshot
The Spatial Control of Cell Differentiation by Autocatalysis and Lateral Inhibition
inferredcites →https://doi.org/10.1007/978-3-642-66784-8_6openalex-snapshot
Cooperative Effects in Fluid Problems
inferredcites →https://doi.org/10.1007/978-3-642-88338-5openalex-snapshot
Synergetics: An Introduction. Nonequilibrium Phase Transitions and Self- Organization in Physics, Chemistry and Biology
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/bf01315081openalex-snapshot
Generalized Ginzburg-Landau equations for phase transition-like phenomena in lasers, nonlinear optics, hydrodynamics and chemical reactions
inferredcites →https://doi.org/10.1007/bf01316549openalex-snapshot
Higher order corrections to generalized ginzburg-Landau Equations of non-equilibrium systems
inferredcites →https://doi.org/10.1007/bf01325461openalex-snapshot
Higher order corrections to generalized Ginzburg-Landau equations of non-equilibrium systems
inferredcites →https://doi.org/10.1007/bf02459528openalex-snapshot
Models for cell differentiation and generation of polarity in diffusion-governed morphogenetic fields
inferredcites →https://doi.org/10.1017/s0022112067001661openalex-snapshot
The stability of finite amplitude cellular convection and its relation to an extremum principle
inferredcites →https://doi.org/10.1017/s0022112069000176openalex-snapshot
Finite bandwidth, finite amplitude convection
inferredcites →https://doi.org/10.1017/s0022112070001921openalex-snapshot
Thermal instabilities in rapidly rotating systems
inferredcites →https://doi.org/10.1017/s0022112071002337openalex-snapshot
Non-linear wave-number interaction in near-critical two-dimensional flows
inferredcites →https://doi.org/10.1017/s0022112075002947openalex-snapshot
Patterns of convection in spherical shells
inferredcites →https://doi.org/10.1063/1.30356openalex-snapshot
Application of nonlinear stability theory to the study of the effects of diffusion on predator-prey interactions
inferredcites →https://doi.org/10.1080/00036817608839125openalex-snapshot
Uniqueness theorems for the compressible flow equation
inferredcites →https://doi.org/10.1098/rstb.1952.0012openalex-snapshot
The chemical basis of morphogenesis
inferredcites →https://doi.org/10.1137/0132032openalex-snapshot
A Model Biochemical Reaction Exhibiting Secondary Bifurcation
inferredcites →https://doi.org/10.1137/1017005openalex-snapshot
On Boundary Layer Problems Exhibiting Resonance
inferredcites →https://doi.org/10.1242/jcs.15.2.321openalex-snapshot
Applications of a theory of biological pattern formation based on lateral inhibition

What points at this work

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

inferred← citeshttps://doi.org/10.1002/9780470141687.ch5openalex-snapshot
Spatial Patterns and Spatiotemporal Dynamics in Chemical Systems
inferred← citeshttps://doi.org/10.1002/bbpc.19850890604openalex-snapshot
Some Basic Concepts of Synergetics with Respect to Pattern Formation. Morphogenesis of Behavior
inferred← citeshttps://doi.org/10.1002/mma.1670010307openalex-snapshot
Stationary solutions of reaction‐diffusion equations
inferred← citeshttps://doi.org/10.1007/978-1-4471-5526-3_1openalex-snapshot
Introduction
inferred← citeshttps://doi.org/10.1007/978-1-4471-5526-3_7openalex-snapshot
The Gierer-Meinhardt System with Inhomogeneous Coefficients
inferred← citeshttps://doi.org/10.1007/978-1-4684-3833-8_29openalex-snapshot
Symmetry Breaking in Embryology and in Neurobiology
inferred← citeshttps://doi.org/10.1007/978-1-4899-7980-3_13openalex-snapshot
Turing Patterns and Excitable Media
inferred← citeshttps://doi.org/10.1007/978-3-319-00254-5_2openalex-snapshot
The Cause of Complexity in Nature: An Analytical and Computational Approach
inferred← citeshttps://doi.org/10.1007/978-3-642-45553-7_1openalex-snapshot
Introduction
inferred← citeshttps://doi.org/10.1007/978-3-642-72758-0_1openalex-snapshot
Contributions of Hermann Haken to Our Understanding of Coherence and Selforganization in Nature
inferred← citeshttps://doi.org/10.1007/978-3-642-76877-4_2openalex-snapshot
Synergetics – Can It Help Physiology
inferred← citeshttps://doi.org/10.1007/978-3-642-76945-0_20openalex-snapshot
From Physics to Synergetics
inferred← citeshttps://doi.org/10.1007/978-3-642-84781-3_1openalex-snapshot
On the Principles of Synergetics
inferred← citeshttps://doi.org/10.1007/978-3-642-87893-0_30openalex-snapshot
Selection of Molecular Species by Competition for a Common Source
inferred← citeshttps://doi.org/10.1007/978-3-642-88338-5_10openalex-snapshot
Applications to Biology
inferred← citeshttps://doi.org/10.1007/978-3-642-96363-6_10openalex-snapshot
Applications to Biology
inferred← citeshttps://doi.org/10.1007/978-3-642-96663-7_10openalex-snapshot
Anwendungen in der Biologie
inferred← citeshttps://doi.org/10.1007/978-3-642-96775-7_10openalex-snapshot
Anwendungen in der Biologie
inferred← citeshttps://doi.org/10.1007/978-3-662-10184-1_1openalex-snapshot
An Introduction
inferred← citeshttps://doi.org/10.1007/978-3-662-10184-1_2openalex-snapshot
Advanced Topics
inferred← citeshttps://doi.org/10.1007/978-3-662-10186-5_10openalex-snapshot
Anwendungen in der Biologie
inferred← citeshttps://doi.org/10.1007/978-3-663-05242-5_13openalex-snapshot
Wenn das Turing wüßte
inferred← citeshttps://doi.org/10.1007/978-94-011-1156-0_10openalex-snapshot
Turing Bifurcations and Pattern Selection
inferred← citeshttps://doi.org/10.1007/978-94-011-1156-0_8openalex-snapshot
Onset and Beyond Turing Pattern Formation
inferred← citeshttps://doi.org/10.1007/bf00276504openalex-snapshot
A collocation approach to the numerical calculation of simple gradients in reaction-diffusion systems
inferred← citeshttps://doi.org/10.1007/bf00285343openalex-snapshot
Temporal organization in a morphogenetic field
inferred← citeshttps://doi.org/10.1007/bf00378014openalex-snapshot
Entwicklungslinien der Synergetik, II
inferred← citeshttps://doi.org/10.1007/bf00700627openalex-snapshot
Qualitative mathematical discussion of different evolutionary states in water transport systems of plants
inferred← citeshttps://doi.org/10.1007/bf01073611openalex-snapshot
Synergetics
inferred← citeshttps://doi.org/10.1007/bf01832840openalex-snapshot
Pattern formation in morphogenesis
inferred← citeshttps://doi.org/10.1007/bf02458822openalex-snapshot
A non-linear analysis for spatial structure in a reaction-diffusion model
inferred← citeshttps://doi.org/10.1007/bf02460024openalex-snapshot
Pattern formation and morphogenesis: A reaction-diffusion model
inferred← citeshttps://doi.org/10.1007/bf02462200openalex-snapshot
Morphogen pattern formation and development in growth
inferred← citeshttps://doi.org/10.1007/s11071-016-3317-9openalex-snapshot
Pattern dynamics of a Gierer–Meinhardt model with spatial effects
inferred← citeshttps://doi.org/10.1016/0009-2614(91)85117-fopenalex-snapshot
A class of reaction-diffusion mechanisms which preferentially select striped patterns
inferred← citeshttps://doi.org/10.1016/0022-5193(83)90401-0openalex-snapshot
A pre-pattern formation mechanism for the spiral-type patterns of the sunflower head
inferred← citeshttps://doi.org/10.1016/0025-5564(85)90075-6openalex-snapshot
Mathematical analysis of an activation-inhibition system in a discrete field
inferred← citeshttps://doi.org/10.1016/0079-6107(82)90019-0openalex-snapshot
Generation of biological patterns and form: Some physical, mathematical, and logical aspects
inferred← citeshttps://doi.org/10.1016/0270-0255(87)90651-8openalex-snapshot
Pattern generation and morphogenesis — a bifurcation analysis
inferred← citeshttps://doi.org/10.1016/0303-2647(92)90026-uopenalex-snapshot
Formation of a regular dissipative structure: a bifurcation and non-linear analysis
inferred← citeshttps://doi.org/10.1016/0303-2647(93)90079-ropenalex-snapshot
Turing structure during embryogenesis
inferred← citeshttps://doi.org/10.1016/0378-4371(92)90262-oopenalex-snapshot
Numerical studies of Turing patterns selection in a two-dimensional system
inferred← citeshttps://doi.org/10.1016/j.apm.2017.01.081openalex-snapshot
Pattern dynamics in a Gierer–Meinhardt model with a saturating term
inferred← citeshttps://doi.org/10.1016/j.na.2010.04.031openalex-snapshot
Transitions and heteroclinic cycles in the general Gierer–Meinhardt equation and cardiovascular calcification model
inferred← citeshttps://doi.org/10.1016/s0034-6667(98)00016-5openalex-snapshot
Computer simulations as a tool for understanding the evolution of water transport systems in land plants: a review and new data
inferred← citeshttps://doi.org/10.1016/s0895-7177(96)00178-1openalex-snapshot
Effect of preassigned gradient on pattern formation and morphogenesis during embryogenesis
inferred← citeshttps://doi.org/10.1023/a:1005764514684openalex-snapshot
Effect of Cross-Diffusion on Pattern Formation – a Nonlinear Analysis
inferred← citeshttps://doi.org/10.1038/352610a0openalex-snapshot
Transition from a uniform state to hexagonal and striped Turing patterns
inferred← citeshttps://doi.org/10.1063/1.462450openalex-snapshot
Conventional and unconventional Turing patterns
inferred← citeshttps://doi.org/10.1063/1.4756213openalex-snapshot
The cause of complexity in nature: An analytical and computational approach
inferred← citeshttps://doi.org/10.1088/0034-4885/52/5/001openalex-snapshot
Synergetics: an overview
inferred← citeshttps://doi.org/10.1103/physreve.94.062217openalex-snapshot
Noisy-flow-induced instability in a reaction-diffusion system
inferred← citeshttps://doi.org/10.1103/physreve.97.022213openalex-snapshot
Nonequilibrium transition and pattern formation in a linear reaction-diffusion system with self-regulated kinetics
inferred← citeshttps://doi.org/10.1103/revmodphys.65.851openalex-snapshot
Pattern formation outside of equilibrium
inferred← citeshttps://doi.org/10.1103/revmodphys.66.1481openalex-snapshot
Biological pattern formation: from basic mechanisms to complex structures
inferred← citeshttps://doi.org/10.1103/vzsr-qztgopenalex-snapshot
Landscape description of the dynamics of Turing patterns
inferred← citeshttps://doi.org/10.1111/j.1939-7445.1998.tb00304.xopenalex-snapshot
DIFFUSION‐DRIVEN INSTABILITY IN THE GIERER‐MEINHARDT MODEL OF MORPHOGENESIS
inferred← citeshttps://doi.org/10.1142/s0218127402005881openalex-snapshot
DIFFUSIVE INSTABILITIES AND CHEMICAL REACTIONS
inferred← citeshttps://doi.org/10.1142/s021812749800187xopenalex-snapshot
Edge of Chaos and Local Activity Domain of the Gierer–Meinhardt CNN
inferred← citeshttps://doi.org/10.1216/rmj-2008-38-5-1493openalex-snapshot
Stability of the $T$ -Periodic Solution on the ES-S Model
inferred← citeshttps://doi.org/10.2748/tmj/1178229312openalex-snapshot
A priori estimates for stationary solutions of an activator-inhibitor model due to Gierer and Meinhardt
inferred← citeshttps://doi.org/10.3389/fnetp.2026.1736738openalex-snapshot
Self-organisation of complex dynamical systems: from synergetics to neuromorphic systems
inferred← citeshttps://doi.org/10.3934/dcdsb.2024024openalex-snapshot
Pattern dynamics of a predator-prey system with Ivlev-type functional response
inferred← citeshttps://doi.org/10.3934/dcdss.2021119openalex-snapshot
The amplitude system for a Simultaneous short-wave Turing and long-wave Hopf instability
inferred← citeshttps://doi.org/10.48550/arxiv.0706.2309openalex-snapshot
Formation and Persistence of Spatiotemporal Turing Patterns
Editorial review for independent work. ICSAC — the Institute for Complexity Science and Advanced Computing — runs a structured editorial panel for researchers publishing outside journals, and publishes on CiteStamp rails. Submission is free and goes through ORCID: icsacinstitute.org/submit.