Varieties of spiral wave behavior: An experimentalist’s approach to the theory of excitable media

Chemical Oscillations, Waves, and Turbulence

1984 • 7,101 citations

Impulses and Physiological States in Theoretical Models of Nerve Membrane

1961 • 5,825 citations

The Geometry of Biological Time

1980 • 3,627 citations

Theory and applications of Hopf bifurcation

1981 • 2,500 citations

Cardiac Electrophysiology: From Cell to Bedside

1991 • 2,234 citations

Electrophysiology of the Heart.

1960 • 1,295 citations

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

1988 • 739 citations

Spatiotemporal concentration patterns in a surface reaction: Propagating and standing waves, rotating spirals, and turbulence

1990 • 727 citations

Spiral Calcium Wave Propagation and Annihilation in Xenopus laevis Oocytes

1991 • 720 citations

Influences of anisotropic tissue structure on reentrant circuits in the epicardial border zone of subacute canine infarcts.

1988 • 513 citations

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

1980 • 458 citations

When time breaks down

1987 • 449 citations

A model for fast computer simulation of waves in excitable media

1991 • 413 citations

Traveling Wave Solutions of a Nerve Conduction Equation

1973 • 412 citations

Defect-mediated turbulence

1989 • 363 citations

Scroll-Shaped Waves of Chemical Activity in Three Dimensions

1973 • 360 citations

Spiral waves in the Belousov-Zhabotinskii reaction

1986 • 351 citations

Simulation of Wave Processes in Excitable Media

1988 • 312 citations

Spiral-wave dynamics in a simple model of excitable media: The transition from simple to compound rotation

1990 • 311 citations

Electrical instability in cardiac muscle: Phase singularities and rotors

1989 • 307 citations

Dynamics of Internal Layers and Diffusive Interfaces

1988 • 289 citations

Rotating Chemical Reactions

1974 • 287 citations

Imaging of spatio-temporal pattern evolution during carbon monoxide oxidation on platinum

1990 • 273 citations

A Cellular Automaton Model of Excitable Media Including Curvature and Dispersion

1990 • 268 citations

A Geometrical Theory for Spiral Waves in Excitable Media

1986 • 266 citations

Chemical vortex dynamics in the Belousov-Zhabotinskii reaction and in the two-variable oregonator model

1989 • 248 citations

Foundations of Synergetics I: Distributed Active Systems

1991 • 210 citations

Computer simulation of arrhythmias in a network of coupled excitable elements.

1980 • 207 citations

Periodic to quasiperiodic transition of chemical spiral rotation

1991 • 188 citations

Waves in Excitable Media

1980 • 173 citations

A SURVEY OF SPIRAL-WAVE BEHAVIORS IN THE OREGONATOR MODEL

1991 • 169 citations

Analytical models of propagation in excitable cells

1976 • 166 citations

RE-ENTRANT ROTATING WAVES IN A BEELER–REUTER BASED MODEL OF TWO-DIMENSIONAL CARDIAC ELECTRICAL ACTIVITY

1991 • 165 citations

Theory of Heart: Biomechanics, Biophysics, and Nonlinear Dynamics of Cardiac Function

2011 • 165 citations

Discrete models for chemically reacting systems

1991 • 154 citations

Perturbation analysis of an approximation to the Hodgkin-Huxley theory

1975 • 152 citations

Non-Equilibrium Dynamics in Chemical Systems

1984 • 150 citations

A cellular automaton model of excitable media

1990 • 140 citations

Cyclic AMP waves during aggregation of Dictyostelium amoebae

1989 • 119 citations

Kinematical theory of spiral waves in excitable media: Comparison with numerical simulations

1991 • 119 citations

Rotating Spiral Wave Solutions of Reaction-Diffusion Equations

1978 • 109 citations

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

1984 • 103 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

Interactions and dynamics of topological defects: Theory and experiments near the onset of weak turbulence

1989 • 94 citations

Meandering transition in two-dimensional excitable media

1990 • 93 citations

Spiral wave dynamics as a function of proton concentration in the ferroin-catalyzed Belousov-Zhabotinskii reaction

1990 • 86 citations

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

1981 • 85 citations

Cell to cell signalling : from experiments to theoretical models

1989 • 84 citations

Spiral breakup in a new model of discrete excitable media

1991 • 82 citations

Chemical vortex dynamics in three-dimensional excitable media

1988 • 81 citations

Model for spiral wave formation in excitable media

1988 • 77 citations

The relationship of excitability to conduction velocity in canine Purkinje tissue.

1978 • 75 citations

Luther's 1906 discovery and analysis of chemical waves

1987 • 72 citations

Mathematical approaches to cardiac arrhythmias.

1990 • 72 citations

Integral Methods in Science and Engineering

1986 • 71 citations

Universal limit of spiral wave propagation in excitable media

1991 • 71 citations

Alternative stable rotors in an excitable medium

1991 • 69 citations

Helical organizing centers in excitable media

1990 • 67 citations

Self-generation of turbulent vortices in a two-dimensional model of cardiac tissue

1990 • 67 citations

Impulse patterning and relaxation propagation in excitable media

1990 • 65 citations

Stable three-dimensional action potential circulation in the Fitzhugh-Nagumo model

1990 • 62 citations

Stably Rotating Patterns of Reaction and Diffusion

1978 • 62 citations

SPATIOTEMPORAL IRREGULARITY IN A TWO-DIMENSIONAL MODEL OF CARDIAC TISSUE

1991 • 62 citations

Curvature and spiral geometry in aggregation patterns of Dictyostelium discoideum

1990 • 61 citations

Anisotropic Reentry in the Epicardial Border Zone of Myocardial Infarcts^a

1990 • 60 citations

Anisotropic conduction properties of canine ventricular muscles. Influence of high extracellular K+ concentration and stimulation frequency.

1985 • 59 citations

Three-dimensional scroll ring dynamics in the Belousov-Zhabotinskii reagent and in the two-variable Oregonator model

1989 • 58 citations

Mathematical models of cardiac arrhythmias (spiral waves)

1978 • 57 citations

[Mechanism of formation of closed propagation pathways in excitable media].

1972 • 55 citations

Understanding the patterns in the BZ reagent

1985 • 54 citations

Diffusive Effects on Dispersion in Excitable Media

1989 • 54 citations

Rotating spiral waves in excitable media: The analytical results

1983 • 52 citations

Waves and Patterns in Chemical and Biological Media

1991 • 51 citations

Spiral waves in a model of myocardium

1987 • 50 citations

Nonlinear Waves in Active Media

1989 • 49 citations

Analysis of meandering in Zykov kinetics

1989 • 49 citations

Transition from circular to linear rotation of a vortex in an excitable cellular medium

1990 • 49 citations

The simplified FitzHugh-Nagumo model with action potential duration restitution: Effects on 2D wave propagation

1991 • 48 citations

Vortices with linear cores in excitable media

1992 • 46 citations

Wave front interaction in steadily rotating spirals

1991 • 46 citations

A cellular automaton model of excitable media

1990 • 41 citations

Spatial stability of traveling wave solutions of a nerve conduction equation

1975 • 39 citations

The Core of the Spiral

1992 • 34 citations

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

1982 • 34 citations

Spiral waves in a model of the ferroin catalyzed Belousov-Zhabotinskii reaction

1986 • 33 citations

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

1979 • 33 citations

Spiral Wave Solutions of Practical Reaction-Diffusion Systems

1980 • 31 citations

[Instabilities of autowaves in excitable media associated with critical curvature phenomena].

1983 • 31 citations

Stability of vortex rotation in an excitable cellular medium

1991 • 30 citations

Analysis of the three-dimensional time-dependent Landau-Ginzburg equation and its solutions

1989 • 28 citations

Target and spiral waves in oscillatory media in the presence of obstacles

1991 • 28 citations

Effect of diffusion on patterns in excitable Belousov-Zhabotinskii systems

1989 • 26 citations

Numerical Study of Vortex Motion in the Two Dimensional Ginzburg-Landau Equation

1989 • 25 citations

Wavelike Activity in Biological and Chemical Media

1974 • 25 citations

The role of curvature and wavefront interactions in spiral-wave dynamics

1991 • 21 citations

A STABLE KNOTTED SINGULARITY IN AN EXCITABLE MEDIUM

1991 • 20 citations

Discrete spectrum of rotor periods in an excitable medium

1990 • 19 citations

Diffusion of autowaves

1989 • 19 citations

Symmetry reduction for the three-dimensional Landau-Ginzburg equation

1988 • 19 citations

A cellular automaton model of excitable media IV. Untwisted scroll rings

1991 • 18 citations

Stable vortex rings of excitation in neuroelectric media

1988 • 16 citations

Effects of tissue geometry on initiation of a cardiac action potential

1989 • 16 citations

[Study of one mechanism of initiation of an ectopic excitation focus using modified Hodgkin-Huxley equations].

1972 • 15 citations

Desynchronization in a Self-Oscillating Medium

1988 • 14 citations

Vortices in Motionless Media

1990 • 14 citations

Reaktionsprodukte yon Oxylsäuremethylester-N-methylamiden mit Antimon(V)-chlorid. Molekülspektren und Struktur / Reaction Products of Oxalic Acid Methylester-N-methylamides and Antimony(V) Chloride. Molecular Spectra and Structure

1979 • 13 citations

Quasi-harmonic rotating waves in distributed active systems

1983 • 13 citations

Dynamics of spiral waves in non-equilibrium media

1990 • 11 citations

Simulation of wave‐propagation in three dimensions using fortran on the CYBER 205

1988 • 11 citations

[Impulse circulation in an excitable medium. Critical size of the closed circuit].

1978 • 8 citations

Schrodinger Equation Approach to Rotating Spiral Waves in Reaction-Diffusion Systems

1982 • 7 citations

[Effect of parameters and properties of an excitable medium on the fibrillation process].

1969 • 3 citations

[Relationship between ionic membrane currents and stationary rates of stable and unstable spike propagation].

1977 • 3 citations

A trial phase function method for a class of λ-ω reaction-diffusion systems: Reduction to a Schrödinger type problem in an eigen sub-domain

1984 • 2 citations

Topological invariants and strings in distributed active dynamical systems

1980 • 2 citations