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

A quantitative description of membrane current and its application to conduction and excitation in nerve

1952 • 21,965 citations

The growth of crystals and the equilibrium structure of their surfaces

1951 • 5,195 citations

THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES

1937 • 4,689 citations

The Geometry of Biological Time

1980 • 3,627 citations

Combustion, Flames and Explosions of Gases

1961 • 2,084 citations

Concentration Wave Propagation in Two-dimensional Liquid-phase Self-oscillating System

1970 • 1,839 citations

Spiral Waves of Chemical Activity

1972 • 1,200 citations

Circus movement in rabbit atrial muscle as a mechanism of tachycardia. III. The "leading circle" concept: a new model of circus movement in cardiac tissue without the involvement of an anatomical obstacle.

1977 • 1,069 citations

Oscillations and traveling waves in chemical systems

1986 • 701 citations

Circus movement in rabbit atrial muscle as a mechanism of trachycardia.

1973 • 689 citations

Circus movement in rabbit atrial muscle as a mechanism of tachycardia. II. The role of nonuniform recovery of excitability in the occurrence of unidirectional block, as studied with multiple microelectrodes.

1976 • 484 citations

Target patterns in a realistic model of the Belousov–Zhabotinskii reaction

1980 • 458 citations

Frequency Plateaus in a Chain of Weakly Coupled Oscillators, I.

1984 • 456 citations

Circus Movement in Rabbit Atrial Muscle as a Mechanism of Tachycardia

1973 • 453 citations

When time breaks down

1987 • 449 citations

Experimental and Theoretical Studies of Flame-Front Stability

1951 • 418 citations

Traveling Wave Solutions of a Nerve Conduction Equation

1973 • 412 citations

Adenosine 3′,5′-Monophosphate Waves in Dictyostelium discoideum : a Demonstration by Isotope Dilution—Fluorography

1981 • 393 citations

Spiral Waves in Reaction-Diffusion Equations

1982 • 387 citations

THE GEOMETRY OF BIOLOGICAL TIME

1981 • 382 citations

On the spatial spread of rabies among foxes

1986 • 366 citations

Scroll-Shaped Waves of Chemical Activity in Three Dimensions

1973 • 360 citations

A cytoplasmic clock with the same period as the division cycle in Xenopus eggs.

1980 • 358 citations

Spiral waves in the Belousov-Zhabotinskii reaction

1986 • 351 citations

The wavelength of the cardiac impulse and reentrant arrhythmias in isolated rabbit atrium. The role of heart rate, autonomic transmitters, temperature, and potassium.

1986 • 333 citations

Signal Propagation during Aggregation in the Slime Mould Dictyostelium discoideum

1974 • 324 citations

A Model Based on Receptor Desensitization for Cyclic AMP Signaling in Dictyostelium Cells

1987 • 301 citations

Biological and Biochemical Oscillators

1973 • 293 citations

Autowave processes in a distributed chemical system

1973 • 292 citations

Rotating Chemical Reactions

1974 • 287 citations

Spiral waves of spreading depression in the isolated chicken retina

1983 • 280 citations

A Geometrical Theory for Spiral Waves in Excitable Media

1986 • 266 citations

Detailed studies of propagating fronts in the iodate oxidation of arsenous acid

1982 • 203 citations

Chemical Waves

1988 • 196 citations

The Structure of the Core of the Spiral Wave in the Belousov-Zhabotinskii Reaction

1985 • 196 citations

The dynamics of three-dimensional scroll waves in excitable media

1988 • 188 citations

Oscillations in chemical systems. V. Quantitative explanation of band migration in the Belousov-Zhabotinskii reaction

1974 • 185 citations

Waves in Excitable Media

1980 • 173 citations

Organizing centres for three-dimensional chemical waves

1984 • 160 citations

Urocyon cinereoargenteus

1982 • 155 citations

Perturbation analysis of an approximation to the Hodgkin-Huxley theory

1975 • 152 citations

Theory of propagation of discontinuities in kinetic systems with multiple time scales: Fronts, front multiplicity, and pulses

1975 • 150 citations

Spiral waves of cyclic amp in a model of slime mold aggregation

1989 • 140 citations

Pattern formation in reacting and diffusing systems

1976 • 138 citations

On a variety of wave phenomena in chemical reactions

1974 • 132 citations

Three-dimensional chemical waves in the Belousov–Zhabotinskii reaction

1983 • 126 citations

Simulation of the electrical and mechanical gradient of the small intestine

1968 • 126 citations

II. Sitzung am Dienstag, den 22. Mai, vormittags 9 Uhr, im grossen Auditorium des chemischen Laboratoriums der Technischen Hochschule. Räumliche Fortpflanzung chemischer Reaktionen

1906 • 122 citations

Cyclic AMP waves during aggregation of Dictyostelium amoebae

1989 • 119 citations

Curvature and Propagation Velocity of Chemical Waves

1988 • 117 citations

Percolation and Galaxies

1986 • 115 citations

A quantitative study of chemical waves in the Belousov–Zhabotinsky reaction

1985 • 113 citations

Phase waves in oscillatory chemical reactions

1973 • 112 citations

The transition from phase waves to trigger waves in a model of the Zhabotinskii reaction

1979 • 109 citations

Signal emission and signal propagation during early aggregation in Dictyostelium discoideum

1976 • 108 citations

Two-dimensional spectrophotometry of spiral wave propagation in the Belousov-Zhabotinskii reaction

1987 • 103 citations

Rotating spiral waves in a modified Fitz-Hugh-Nagumo model

1984 • 103 citations

A New Laser Scanning System for Measuring Action Potential Propagation in the Heart

1981 • 97 citations

Two regimes of the scroll ring drift in the three-dimensional active media

1987 • 95 citations

Dispersion of traveling waves in the belousov-zhabotinskii reaction

1988 • 95 citations

Horizontal Bands in the Belousov Reaction

1973 • 89 citations

Traveling waves in the nitric acid-iron(II) reaction

1985 • 87 citations

Dictyostelium discoideum aggregation fields as excitable media

1973 • 86 citations

Propagation of chemical reactions in space

1987 • 86 citations

Target pattern and spiral solutions to reaction-diffusion equations with more than one space dimension

1981 • 85 citations

Singular filaments organize chemical waves in three dimensions

1983 • 84 citations

Solubility and diffusion coefficient of adenosine 3':5'-monophosphate.

1977 • 81 citations

Die folgen einiger elektronenträgheitseffekte in elektronenrohren II

1942 • 80 citations

Combustion flames and explosions of gases

1988 • 79 citations

Pattern Formation in Oscillatory Chemical Reactions

1976 • 79 citations

Model for spiral wave formation in excitable media

1988 • 77 citations

Luther's 1906 discovery and analysis of chemical waves

1987 • 72 citations

Target patterns in reaction-diffusion systems

1981 • 71 citations

Stably Rotating Patterns of Reaction and Diffusion

1978 • 62 citations

Two-dimensional spectrophotometry and pseudo-color representation of chemical reaction patterns

1986 • 61 citations

Two kinds of wave in an oscillating chemical solution

1974 • 61 citations

Chemical waves in a two-dimensional oscillating system

1983 • 59 citations

Circulation of cortical spreading depression around electrically stimulated areas and epileptic foci in the neocortex of rats

1979 • 58 citations

Mathematical Problems in Biology

1974 • 58 citations

Two-dimensional spectrophotometry of spiral wave propagation in the Belousov-Zhabotinskii reaction

1987 • 57 citations

Singular filaments organize chemical waves in three dimensions

1983 • 56 citations

The Landscape Epidemiology of Rabies in Virginia

1978 • 56 citations

Target Patterns and Horseshoes from a Perturbed Central‐Force Problem: Some Temporally Periodic Solutions to Reaction‐Diffusion Equations

1981 • 55 citations

Diffusive Effects on Dispersion in Excitable Media

1989 • 54 citations

Singular filaments organize chemical waves in three dimensions II. Twisted waves

1983 • 54 citations

Singular filaments organize chemical waves in three dimensions

1984 • 54 citations

Non-equilibrium dynamics in chemical systems

1985 • 53 citations

Rotating spiral waves in excitable media: The analytical results

1983 • 52 citations

Simulated propagation of cardiac action potentials

1980 • 52 citations

Spiral waves in a model of myocardium

1987 • 50 citations

Rotating waves as asymptotic solutions of a model chemical reaction

1977 • 49 citations

The Motion of Untwisted Untorted Scroll Waves in Belousov-Zhabotinsky Reagent

1988 • 49 citations

On the nonlinear thermal diffusive theory of curved flames

1987 • 48 citations

Measurement of dispersion relation of chemical waves in an oscillatory reacting medium

1988 • 46 citations

Self-organizing Structures

1987 • 43 citations

[Vortex ring in a 3-dimensional active medium described by reaction-diffusion equations].

1984 • 42 citations

Dynamical simulations of twisted scroll rings in three-dimensional excitable media

1985 • 42 citations

Propagator-Controller Systems and Chemical Patterns

1984 • 40 citations

Twisted scroll waves in active three-dimensional media

1985 • 39 citations

Stationary concentration patterns in the Oregonator model of the Belousov-Zhabotinskii reaction

1985 • 39 citations

Turbulent rings in 3-dimensional active media with diffusion by 2 components

1986 • 39 citations

Periodic Solutions to Reaction-Diffusion Equations

1976 • 38 citations

A novel moving boundary reaction involving hydroxylamine and nitric acid

1983 • 37 citations

On the formation of circulating patterns of excitation in anisotropic excitable media

1988 • 36 citations

Rotating Spiral Waves in Reaction-Diffusion Systems: Phase Singularities of Multi-Armed Waves

1982 • 34 citations

Wave profile and speed near the core of a target pattern in the Belousov-Zhabotinsky reaction

1987 • 34 citations

Winfree Meandering in a 2-Dimensional 2-Variable Excitable Medium

1979 • 33 citations

A computational study of twisted linked scroll waves in excitable media

1987 • 32 citations

Spiral Wave Solutions of Practical Reaction-Diffusion Systems

1980 • 31 citations

Stability of periodic travelling wave solutions of a nerve conduction equation

1978 • 29 citations

Three-dimensional waves in excitable reaction-diffusion systems

1987 • 27 citations

Wavelike Activity in Biological and Chemical Media

1974 • 25 citations

Etude expérimentale statistique des structures cibles de la réaction de Belousov-Zhabotinsky en régime oscillant

1986 • 25 citations

AN EXPERIMENTAL STUDY OF CHEMICAL WAVE PROPAGATION

1973 • 24 citations

Spatial waves in the reaction of chlorite with iodide

1984 • 23 citations

Spatial Effects in Active Chemical Systems. I. Model of Leading Center

1977 • 18 citations

Knotted scroll wave filaments in excitable media

1989 • 15 citations

The Speed of Propagation of Oxidizing and Reducing Wave Fronts in the Belousov-Zhabotinskii Reaction

1984 • 14 citations

Rotating waves in reaction-diffusion systems with folded slow manifolds

1986 • 10 citations

OSCILLATORY BEHAVIOR, EXCITABILITY AND PROPAGATION PHENOMENA ON MEMBRANES AND MEMBRANE-LIKE INTERFACES

1973 • 9 citations

Static reaction–diffusion structures in folded slow manifold systems

1986 • 8 citations

Coupled Oscillators and Locomotion by Fish

1986 • 4 citations