On the public citation graph

Pattern sensitivity to boundary and initial conditions in reaction-diffusion models

0 signed · 118 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 See whether every reference in this work resolves to a known work and none has been retracted — and get a dated CiteStamped badge you can embed.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/bf00275801openalex-snapshot
Nonhomogeneous spatial distributions of populations
inferredcites →https://doi.org/10.1016/0014-5793(77)80777-1openalex-snapshot
Analysis and control of immobilized enzyme systems
inferredcites →https://doi.org/10.1016/0022-5193(72)90018-5openalex-snapshot
The dynamics of cellular differentiation and associated pattern formation
inferredcites →https://doi.org/10.1016/0022-5193(74)90128-3openalex-snapshot
How well does Turing's theory of morphogenesis work?
inferredcites →https://doi.org/10.1016/0022-5193(77)90216-8openalex-snapshot
Thresholds in development
inferredcites →https://doi.org/10.1016/0022-5193(79)90042-0openalex-snapshot
Simple chemical reaction systems with limit cycle behaviour
inferredcites →https://doi.org/10.1016/0022-5193(81)90334-9openalex-snapshot
A Pre-pattern formation mechanism for animal coat markings
inferredcites →https://doi.org/10.1016/0022-5193(82)90063-7openalex-snapshot
Parameter space for turing instability in reaction diffusion mechanisms: A comparison of models
inferredcites →https://doi.org/10.1016/0079-6107(82)90019-0openalex-snapshot
Generation of biological patterns and form: Some physical, mathematical, and logical aspects
inferredcites →https://doi.org/10.1016/0167-2789(81)90032-4openalex-snapshot
A mathematical model for pattern formation in biological systems
inferredcites →https://doi.org/10.1016/bs.ctdb.2015.11.008openalex-snapshot
Positional Information and Pattern Formation
inferredcites →https://doi.org/10.1016/s0022-5193(80)80024-5openalex-snapshot
Pattern formation by reaction-diffusion instabilities: Application to morphogenesis in Drosophila
inferredcites →https://doi.org/10.1063/1.439761openalex-snapshot
Dissipative structures in reaction–diffusion systems: Numerical determination of bifurcations in the sphere
inferredcites →https://doi.org/10.1098/rstb.1952.0012openalex-snapshot
The chemical basis of morphogenesis
inferredcites →https://doi.org/10.1098/rstb.1981.0155openalex-snapshot
On pattern formation mechanisms for lepidopteran wing patterns and mammalian coat markings
inferredcites →https://doi.org/10.1126/science.413193openalex-snapshot
Control of Sequential Compartment Formation in Drosophila
inferredcites →https://doi.org/10.1201/9781420083583openalex-snapshot
Differential Equations and Mathematical Biology
inferredcites →https://doi.org/10.1515/zna-1976-0710openalex-snapshot
Chemical Oscillations by Substrate Inhibition
inferredcites →https://doi.org/10.2307/2005674openalex-snapshot
Numerical Initial Value Problems in Ordinary Differential Equations
inferredcites →https://doi.org/10.2307/2530271openalex-snapshot
Lectures on Nonlinear Differential-Equation Models in Biology

What points at this work

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

inferred← citeshttps://doi.org/10.1006/bulm.1999.0131openalex-snapshot
Reaction and Diffusion on Growing Domains: Scenarios for Robust Pattern Formation
inferred← citeshttps://doi.org/10.1006/jmaa.2000.7314openalex-snapshot
On Conditions for the Stability of a Two Component Mixed Quasimonotone Reaction Diffusion Equation
inferred← citeshttps://doi.org/10.1007/978-1-4613-0133-2_4openalex-snapshot
Models for Pigment Pattern Formation in the Skin of Fishes
inferred← citeshttps://doi.org/10.1007/978-3-319-43669-2_13openalex-snapshot
Turing’s Theory of Morphogenesis: Where We Started, Where We Are and Where We Want to Go
inferred← citeshttps://doi.org/10.1007/978-3-642-45726-5_10openalex-snapshot
Self-Organization, Catastrophe Theory and the Problem of Segmentation
inferred← citeshttps://doi.org/10.1007/978-94-009-2975-3_39openalex-snapshot
Numerical Studies of Symmetry-Breaking Bifurcations in Reaction-Diffusion Systems
inferred← citeshttps://doi.org/10.1007/bf00043976openalex-snapshot
Stable pattern and standing wave formation in a simple isothermal cubic autocatalytic reaction scheme
inferred← citeshttps://doi.org/10.1007/bf00178771openalex-snapshot
Implicit-explicit methods for reaction-diffusion problems in pattern formation
inferred← citeshttps://doi.org/10.1007/bf00709367openalex-snapshot
Rational taxonomy and the natural system
inferred← citeshttps://doi.org/10.1007/bf02458442openalex-snapshot
Wavelength selection mechanism in the Gierer-Meinhardt model
inferred← citeshttps://doi.org/10.1007/bf02459571openalex-snapshot
Discussion: Turing's theory of morphogenesis—Its influence on modelling biological pattern and form
inferred← citeshttps://doi.org/10.1007/bf02460782openalex-snapshot
Reliable segmentation by successive bifurcation
inferred← citeshttps://doi.org/10.1007/bf02460888openalex-snapshot
Diffusion driven instability in an inhomogeneous domain
inferred← citeshttps://doi.org/10.1007/s00211-013-0591-zopenalex-snapshot
A three level finite element approximation of a pattern formation model in developmental biology
inferred← citeshttps://doi.org/10.1007/s00285-008-0233-8openalex-snapshot
Steps toward numerical mode analysis of organizing systems
inferred← citeshttps://doi.org/10.1007/s002850100112openalex-snapshot
Mode-doubling and tripling in reaction-diffusion patterns on growing domains: A piecewise linear model
inferred← citeshttps://doi.org/10.1007/s10867-017-9450-yopenalex-snapshot
The interplay between phenotypic and ontogenetic plasticities can be assessed using reaction-diffusion models
inferred← citeshttps://doi.org/10.1007/s10884-004-7834-8openalex-snapshot
The Effect of Growth and Curvature on Pattern Formation
inferred← citeshttps://doi.org/10.1007/s11538-006-9066-zopenalex-snapshot
Gene Expression Time Delays and Turing Pattern Formation Systems
inferred← citeshttps://doi.org/10.1007/s11538-007-9230-0openalex-snapshot
Turing Pattern Formation with Two Kinds of Cells and a Diffusive Chemical
inferred← citeshttps://doi.org/10.1007/s11538-010-9533-4openalex-snapshot
Aberrant Behaviours of Reaction Diffusion Self-organisation Models on Growing Domains in the Presence of Gene Expression Time Delays
inferred← citeshttps://doi.org/10.1007/s11538-021-00870-yopenalex-snapshot
Bespoke Turing Systems
inferred← citeshttps://doi.org/10.1007/s11538-021-00913-4openalex-snapshot
Isolating Patterns in Open Reaction–Diffusion Systems
inferred← citeshttps://doi.org/10.1007/s11538-022-01055-xopenalex-snapshot
Boundary Conditions Cause Different Generic Bifurcation Structures in Turing Systems
inferred← citeshttps://doi.org/10.1007/s11538-025-01552-9openalex-snapshot
Persistent Homology Classifies Parameter Dependence of Patterns in Turing Systems
inferred← citeshttps://doi.org/10.1007/s11538-026-01669-5openalex-snapshot
Delayed Pattern Formation in Two-Dimensional Domains
inferred← citeshttps://doi.org/10.1016/b978-0-12-287960-9.50019-8openalex-snapshot
Pattern formation mechanisms – a comparison of reaction-diffusion and mechanochemical models
inferred← citeshttps://doi.org/10.1016/b978-0-12-287960-9.50022-8openalex-snapshot
Bifurcations, harmonics and the four colour wheel model of Drosophila development
inferred← citeshttps://doi.org/10.1016/bs.ctdb.2024.11.008openalex-snapshot
Coordination of nephrogenesis with branching of the urinary collecting system, the vasculature and the nervous system
inferred← citeshttps://doi.org/10.1016/j.cnsns.2011.10.005openalex-snapshot
Stability analysis of an epidemic model with diffusion and stochastic perturbation
inferred← citeshttps://doi.org/10.1016/j.jcp.2005.09.012openalex-snapshot
Time-stepping schemes for moving grid finite elements applied to reaction–diffusion systems on fixed and growing domains
inferred← citeshttps://doi.org/10.1016/j.jmaa.2011.01.057openalex-snapshot
The asymptotic analysis of an insect dispersal model on a growing domain
inferred← citeshttps://doi.org/10.1016/j.matcom.2012.02.009openalex-snapshot
Long-time behavior of the solutions of Murray–Thomas model for interacting chemicals
inferred← citeshttps://doi.org/10.1016/j.mbs.2025.109602openalex-snapshot
Complex dynamics and pattern formation in a diffusive epidemic model with an infection-dependent recovery rate
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/j.nonrwa.2012.01.018openalex-snapshot
Complex dynamics of a reaction–diffusion epidemic model
inferred← citeshttps://doi.org/10.1016/j.physa.2014.06.038openalex-snapshot
Effect of time delay on pattern dynamics in a spatial epidemic model
inferred← citeshttps://doi.org/10.1016/j.physd.2024.134353openalex-snapshot
Boundary conditions influence on Turing patterns under anomalous diffusion: A numerical exploration
inferred← citeshttps://doi.org/10.1016/s0022-5193(05)80078-5openalex-snapshot
Spatial harmonics and pattern specification in early Drosophila development. Part I. Bifurcation sequences and gene expression
inferred← citeshttps://doi.org/10.1016/s0022-5193(05)80079-7openalex-snapshot
Spatial harmonics and pattern specification in early Drosophila development. Part II. The four colour wheels model
inferred← citeshttps://doi.org/10.1016/s0022-5193(05)80622-8openalex-snapshot
Formulation of a morphogenetic model for embryo development in dicotyledonous plants
inferred← citeshttps://doi.org/10.1016/s0022-5193(89)80202-4openalex-snapshot
Wavelike isomorphic prepatterns in development
inferred← citeshttps://doi.org/10.1016/s0074-7696(08)60510-0openalex-snapshot
Cellular Mechanisms of Pattern Formation in the Developing Limb
inferred← citeshttps://doi.org/10.1016/s0074-7696(08)61545-4openalex-snapshot
Appendix: Dialogue on Embryonic Induction and Differentiation Waves
inferred← citeshttps://doi.org/10.1016/s0092-8240(02)00098-8openalex-snapshot
Mathematical Models of Cell Colonization of Uniformly Growing Domains
inferred← citeshttps://doi.org/10.1016/s0092-8240(05)80007-2openalex-snapshot
: Turing's theory of morphogenesis—Its influence on modelling biological pattern and form
inferred← citeshttps://doi.org/10.1016/s0096-3003(03)00295-9openalex-snapshot
Symmetric patterns in the Dirichlet problem for a two-cell cubic autocatalytor reaction model
inferred← citeshttps://doi.org/10.1016/s0167-2789(01)00345-1openalex-snapshot
Parameter space analysis, pattern sensitivity and model comparison for Turing and stationary flow-distributed waves (FDS)
inferred← citeshttps://doi.org/10.1016/s0304-3800(96)00005-1openalex-snapshot
Population-dynamic instability as a cause of patch structure
inferred← citeshttps://doi.org/10.1016/s0375-9601(96)00688-3openalex-snapshot
Theory of self-replication and granulation of spike autosolitons
inferred← citeshttps://doi.org/10.1016/s0895-7177(96)00174-4openalex-snapshot
Modelling the role of cell-cell adhesion in the growth and development of carcinomas
inferred← citeshttps://doi.org/10.1016/s0924-6509(08)70043-6openalex-snapshot
Mathematical Analysis of a Competitive Network for Attention
inferred← citeshttps://doi.org/10.1017/s0956792526100515openalex-snapshot
Role of dimension and geometry: non-uniqueness in the pseudo-one-dimensional limit for Turing patterns on parallelograms
inferred← citeshttps://doi.org/10.1023/a:1019159427561openalex-snapshot
On the origin of Turing instability
inferred← citeshttps://doi.org/10.1038/nphys4155openalex-snapshot
Self-organization and positioning of bacterial protein clusters
inferred← citeshttps://doi.org/10.1051/mmnp/20094401openalex-snapshot
The Intersection of Theory and Application in Elucidating Pattern Formation in Developmental Biology
inferred← citeshttps://doi.org/10.1063/1.4921767openalex-snapshot
Helical Turing patterns in the Lengyel-Epstein model in thin cylindrical layers
inferred← citeshttps://doi.org/10.1073/pnas.0308436101openalex-snapshot
Pattern formation by vascular mesenchymal cells
inferred← citeshttps://doi.org/10.1073/pnas.0607790104openalex-snapshot
Pattern regulation in the stripe of zebrafish suggests an underlying dynamic and autonomous mechanism
inferred← citeshttps://doi.org/10.1073/pnas.1313083111openalex-snapshot
Predicting the spatiotemporal dynamics of hair follicle patterns in the developing mouse
inferred← citeshttps://doi.org/10.1073/pnas.96.10.5549openalex-snapshot
Stripe formation in juvenile Pomacanthus explained by a generalized Turing mechanism with chemotaxis
inferred← citeshttps://doi.org/10.1080/02681118908806076openalex-snapshot
Pattern formation through reaction and diffusion in a simple pooled-chemical system
inferred← citeshttps://doi.org/10.1088/1367-2630/10/5/055002openalex-snapshot
The formation of labyrinths, spots and stripe patterns in a biochemical approach to cardiovascular calcification
inferred← citeshttps://doi.org/10.1088/1742-5468/2010/11/p11036openalex-snapshot
Pattern selection in a ratio-dependent predator–prey model
inferred← citeshttps://doi.org/10.1088/1751-8121/ab9e8dopenalex-snapshot
Memory effects in fluctuating dynamic density-functional theory: theory and simulations
inferred← citeshttps://doi.org/10.1098/rsfs.2011.0113openalex-snapshot
Turing's model for biological pattern formation and the robustness problem
inferred← citeshttps://doi.org/10.1098/rsfs.2011.0122openalex-snapshot
Towards an integrated experimental–theoretical approach for assessing the mechanistic basis of hair and feather morphogenesis
inferred← citeshttps://doi.org/10.1098/rsif.2023.0276openalex-snapshot
Free energy dissipation enhances spatial accuracy and robustness of self-positioned Turing pattern in small biochemical systems
inferred← citeshttps://doi.org/10.1098/rspa.2016.0744openalex-snapshot
History dependence and the continuum approximation breakdown: the impact of domain growth on Turing’s instability
inferred← citeshttps://doi.org/10.1101/2024.09.09.611947openalex-snapshot
Effects of multistability, absorbing boundaries and growth on Turing pattern formation
inferred← citeshttps://doi.org/10.1103/physreve.102.032214openalex-snapshot
Eckhaus selection: The mechanism of pattern persistence in a reaction-diffusion system
inferred← citeshttps://doi.org/10.1103/physreve.103.012215openalex-snapshot
Pattern selection in reaction diffusion systems
inferred← citeshttps://doi.org/10.1103/physreve.56.185openalex-snapshot
Self-replicating spots in reaction-diffusion systems
inferred← citeshttps://doi.org/10.1103/physreve.84.041923openalex-snapshot
Modeling parr-mark pattern formation during the early development of Amago trout
inferred← citeshttps://doi.org/10.1103/physreve.84.046216openalex-snapshot
Stochastic reaction and diffusion on growing domains: Understanding the breakdown of robust pattern formation
inferred← citeshttps://doi.org/10.1103/physreve.85.021924openalex-snapshot
Spatial dynamics in a predator-prey model with Beddington-DeAngelis functional response
inferred← citeshttps://doi.org/10.1103/physreve.85.066132openalex-snapshot
Regulation of Turing patterns in a spatially extended chlorine–iodine–malonic-acid system with a local concentration-dependent diffusivity
inferred← citeshttps://doi.org/10.1103/physrevlett.72.2797openalex-snapshot
Dynamics of self-replicating patterns in reaction diffusion systems
inferred← citeshttps://doi.org/10.1103/revmodphys.65.851openalex-snapshot
Pattern formation outside of equilibrium
inferred← citeshttps://doi.org/10.1109/icaci.2012.6463317openalex-snapshot
Bifurcation and luring instability of a class of reaction-diffusion neural networks
inferred← citeshttps://doi.org/10.1111/brv.12720openalex-snapshot
The seven ways eukaryotes produce repeated colour motifs on external tissues
inferred← citeshttps://doi.org/10.1111/dgd.12377openalex-snapshot
Role of domain in pattern formation
inferred← citeshttps://doi.org/10.1126/science.1221920openalex-snapshot
Differential Diffusivity of Nodal and Lefty Underlies a Reaction-Diffusion Patterning System
inferred← citeshttps://doi.org/10.1137/17m1138571openalex-snapshot
Domain Size Driven Instability: Self-Organization in Systems with Advection
inferred← citeshttps://doi.org/10.1142/s0218339010003366openalex-snapshot
MEASUREMENT OF SELF-ORGANIZATION IN ARID ECOSYSTEMS
inferred← citeshttps://doi.org/10.1186/s13661-024-01835-5openalex-snapshot
The Robin problems for the coupled system of reaction–diffusion equations
inferred← citeshttps://doi.org/10.1201/9780429493362-12openalex-snapshot
Pattern Formation in Biological Systems
inferred← citeshttps://doi.org/10.1242/dev.104.1.105openalex-snapshot
Theoretical aspects of stripe formation in relation to Drosophila segmentation
inferred← citeshttps://doi.org/10.1371/journal.pone.0201746openalex-snapshot
Curvature-driven spatial patterns in growing 3D domains: A mechanochemical model for phyllotaxis
inferred← citeshttps://doi.org/10.2139/ssrn.5507449openalex-snapshot
Existence of Turing instability in structured clay materials
inferred← citeshttps://doi.org/10.24275/uami.rx913q12bopenalex-snapshot
Patrones de Turing en sistemas biológicos
inferred← citeshttps://doi.org/10.3410/f.718281775.793491289openalex-snapshot
Faculty Opinions recommendation of Predicting the spatiotemporal dynamics of hair follicle patterns in the developing mouse.
inferred← citeshttps://doi.org/10.3934/dcdss.2020433openalex-snapshot
Oscillatory states and patterns formation in a two-cell cubic autocatalytic reaction-diffusion model subjected to the Dirichlet conditions
inferred← citeshttps://doi.org/10.3934/mbe.2020381openalex-snapshot
A hybrid discrete-continuum approach to model Turing pattern formation
inferred← citeshttps://doi.org/10.4171/zaa/1390openalex-snapshot
Global Bifurcation for a Reaction-Diffusion System with Inclusions
inferred← citeshttps://doi.org/10.48550/arxiv.1912.05113openalex-snapshot
Spatial scale of agglomeration and dispersion: Number, spacing, and the spatial extent of cities
inferred← citeshttps://doi.org/10.5194/npg-21-251-2014openalex-snapshot
Synchronization of coupled stick-slip oscillators
inferred← citeshttps://doi.org/10.9734/arrb/2021/v36i530380openalex-snapshot
Spatio-temporal Brusselator Model and Biological Pattern Formation
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.