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Rotating Chemical Waves in the Gray–Scott Model

https://doi.org/10.1137/0152011

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What this work says

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

inferredcites →https://doi.org/10.1007/978-1-4612-1037-5openalex-snapshot

Geometrical Methods in the Theory of Ordinary Differential Equations

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Perturbation Methods, Bifurcation Theory and Computer Algebra

inferredcites →https://doi.org/10.1007/978-1-4612-1140-2openalex-snapshot

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

inferredcites →https://doi.org/10.1007/978-1-4612-4574-2openalex-snapshot

Singularities and Groups in Bifurcation Theory

inferredcites →https://doi.org/10.1007/978-1-4612-5034-0openalex-snapshot

Singularities and Groups in Bifurcation Theory

inferredcites →https://doi.org/10.1007/978-1-4612-6374-6_17openalex-snapshot

Bifurcations with Symmetry

inferredcites →https://doi.org/10.1007/978-1-4684-0147-9openalex-snapshot

Geometrical Methods in the Theory of Ordinary Differential Equations

inferredcites →https://doi.org/10.1007/978-3-0348-6256-1_35openalex-snapshot

The Numerical Calculation of Cusps, Bifurcation Points and Isola Formation Points in Two Parameter Problems

inferredcites →https://doi.org/10.1007/978-3-642-66243-0openalex-snapshot

Elements of the Theory of Representations

inferredcites →https://doi.org/10.1007/bf00247751openalex-snapshot

Bifurcations in the presence of a symmetry group

inferredcites →https://doi.org/10.1007/bf00280698openalex-snapshot

Hopf Bifurcation in the presence of symmetry

inferredcites →https://doi.org/10.1007/bfb0087456openalex-snapshot

Group Theoretic Methods in Bifurcation Theory

inferredcites →https://doi.org/10.1007/bfb0089647openalex-snapshot

Geometric Theory of Semilinear Parabolic Equations

inferredcites →https://doi.org/10.1016/0009-2509(83)80132-8openalex-snapshot

Autocatalytic reactions in the isothermal, continuous stirred tank reactor

inferredcites →https://doi.org/10.1016/0009-2509(84)85056-3openalex-snapshot

Global analysis of the multiplicity features of multi-reaction lumped-parameter systems

inferredcites →https://doi.org/10.1016/0022-0396(81)90045-0openalex-snapshot

Classification and unfoldings of degenerate Hopf bifurcations

inferredcites →https://doi.org/10.1016/0022-0396(87)90119-7openalex-snapshot

A classification of degenerate Hopf bifurcations with O(2) symmetry

inferredcites →https://doi.org/10.1016/0160-9327(86)90067-0openalex-snapshot

Oscillations and traveling waves in chemical systems

inferredcites →https://doi.org/10.1016/0167-2789(87)90049-2openalex-snapshot

A simple global characterization for normal forms of singular vector fields

inferredcites →https://doi.org/10.1016/0167-2789(88)90062-0openalex-snapshot

Singular perturbation theory of traveling waves in excitable media (a review)

inferredcites →https://doi.org/10.1017/s0308210500019223openalex-snapshot

Hopf bifurcation and symmetry: travelling and standing waves on the circle

inferredcites →https://doi.org/10.1017/s0308210500024173openalex-snapshot

Heteroclinic cycles involving periodic solutions in mode interactions with O(2) symmetry

inferredcites →https://doi.org/10.1021/j100247a009openalex-snapshot

Sustained oscillations and other exotic patterns of behavior in isothermal reactions

inferredcites →https://doi.org/10.1038/329619a0openalex-snapshot

Sustained chemical waves in an annular gel reactor: a chemical pinwheel

inferredcites →https://doi.org/10.1063/1.433672openalex-snapshot

Rotating waves as asymptotic solutions of a model chemical reaction

inferredcites →https://doi.org/10.1063/1.451473openalex-snapshot

Complex periodic oscillations and Farey arithmetic in the Belousov–Zhabotinskii reaction

inferredcites →https://doi.org/10.1063/1.453935openalex-snapshot

Sustained spiral waves in a continuously fed unstirred chemical reactor

inferredcites →https://doi.org/10.1080/02681118608806019openalex-snapshot

Hopf-Hopf mode interactions with O(2) symmetry

inferredcites →https://doi.org/10.1090/conm/056/855083openalex-snapshot

Nilpotent normal forms and representation theory of 𝑠𝑙(2,𝑅)

inferredcites →https://doi.org/10.1098/rspa.1987.0061openalex-snapshot

On the steady-state behaviour of the autocatalator model A + 2B⇌3B, B⇌C in a continuous-flow stirred-tank reactor

inferredcites →https://doi.org/10.1098/rsta.1987.0050openalex-snapshot

The Takens-Bogdanov bifurcation with O(2)-symmetry

inferredcites →https://doi.org/10.1111/j.1749-6632.1979.tb29474.xopenalex-snapshot

BIFURCATING WAVES*

inferredcites →https://doi.org/10.1126/science.175.4022.634openalex-snapshot

Spiral Waves of Chemical Activity

inferredcites →https://doi.org/10.1137/0145044openalex-snapshot

Geometrical Characteristics Associated with Stability and Bifurcations of Periodic Travelling Waves in Reaction-Diffusion Systems

inferredcites →https://doi.org/10.1137/0146064openalex-snapshot

Existence of Traveling Wave Trains in Nerve Axon Equations

inferredcites →https://doi.org/10.1137/0150029openalex-snapshot

Patterns of Propagating Pulses

inferredcites →https://doi.org/10.1137/0516083openalex-snapshot

Degenerate Hopf Bifurcation and Nerve Impulse

inferredcites →https://doi.org/10.1137/0520001openalex-snapshot

Degenerate Hopf Bifurcation and Nerve Impulse. Part II

inferredcites →https://doi.org/10.1137/0520002openalex-snapshot

Degenerate Hopf Bifurcation Formulas and Hilbert’s 16th Problem

What points at this work

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

inferred← citeshttps://doi.org/10.1007/s00033-016-0660-0openalex-snapshot

Cubic autocatalysis in a reaction–diffusion annulus: semi-analytical solutions

inferred← citeshttps://doi.org/10.1007/s10884-026-10519-wopenalex-snapshot

Bifurcation of Rotating Wave Solutions in Reaction-Diffusion Systems on a Circle

inferred← citeshttps://doi.org/10.1007/s11075-023-01532-xopenalex-snapshot

A finite difference scheme for the two-dimensional Gray-Scott equation with fractional Laplacian

inferred← citeshttps://doi.org/10.1016/j.apnum.2026.01.001openalex-snapshot

Linearized and high-order accurate one-parameter compact difference schemes for solving the Gray-Scott reaction-diffusion model

inferred← citeshttps://doi.org/10.1016/j.cnsns.2017.01.031openalex-snapshot

Rotating and standing waves in a diffractive nonlinear optical system with delayed feedback under O (2) Hopf bifurcation

inferred← citeshttps://doi.org/10.1016/j.cnsns.2017.08.021openalex-snapshot

Generative complexity of Gray–Scott model

inferred← citeshttps://doi.org/10.1016/j.jcp.2023.112751openalex-snapshot

HomPINNs: Homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions

inferred← citeshttps://doi.org/10.1063/1.467198openalex-snapshot

Analysis of concentration and temperature patterns on catalytic surfaces

inferred← citeshttps://doi.org/10.1080/00102209408935398openalex-snapshot

Hopping Motion in Ordered States of Cellular Flames

inferred← citeshttps://doi.org/10.1080/02681119108806113openalex-snapshot

Hopf-steady-state mode interactions with 0(2) symmetry

inferred← citeshttps://doi.org/10.1103/physreva.46.5054openalex-snapshot

Symmetry-breaking bifurcations in one-dimensional excitable media

inferred← citeshttps://doi.org/10.1115/1.2338324openalex-snapshot

Hopf-Hopf Interactions of Surge and Rotating Stall

inferred← citeshttps://doi.org/10.1142/s0218127417300245openalex-snapshot

Global Bifurcation Map of the Homogeneous States in the Gray–Scott Model

inferred← citeshttps://doi.org/10.48550/arxiv.1610.09097openalex-snapshot

Generative complexity of Gray-Scott model

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