The Dynamics of Scroll Waves in Excitable Media

No abstract is available for this paper.

• Publication year

  1992

• Venue

  SIAM Review

• Publication date

  1992-03-01

• Fields of study

  Mathematics, Physics, Computer Science

• Identifiers
  DOI 10.1137/1034001
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• The core of the spiral

  1992cited by this paper
• Pattern formation in excitable media

  1992cited by this paper
• Spiral core in singly diffusive excitable media.

  1992cited by this paper
• Wave front interaction in steadily rotating spirals

  1991cited by this paper
• Three Dimensional Vortices in Active Media

  1991cited by this paper
• Spiral wave solutions for reaction-diffusion equations in a fast reaction/slow diffusion limit

  1991cited by this paper
• Varieties of spiral wave behavior: An experimentalist's approach to the theory of excitable media.

  1991cited by this paper
• THE DIFFERENTIAL GEOMETRY OF SCROLL WAVES

  1991cited by this paper
• A SURVEY OF SPIRAL-WAVE BEHAVIORS IN THE OREGONATOR MODEL

  1991cited by this paper
• Universal limit of spiral wave propagation in excitable media.

  1991cited by this paper
• A STABLE KNOTTED SINGULARITY IN AN EXCITABLE MEDIUM

  1991cited by this paper
• The dynamics of helical scroll waves in excitable media

  1991cited by this paper
• Analysis of meandering in Zykov kinetics

  1990cited by this paper
• Stable three-dimensional action potential circulation in the FitzHugh-Nagumo model

  1990cited by this paper
• Stable Particle-Like Solutions to the Nonlinear Wave Equations of Three-Dimensional Excitable Media

  1990cited by this paper
• Three-dimensional twisted vortices in an excitable chemical medium

  1990cited by this paper
• Helical organizing centers in excitable media

  1990influential reference
• Dynamical stability of untwisted scroll rings in excitable media

  1989cited by this paper
• An integral invariant for scroll rings in a reaction-diffusion system

  1989cited by this paper
• Three-dimensional scroll ring dynamics in the Belousov-Zhabotinskii reagent and in the two-variable Oregonator model

  1989cited by this paper
• Chemical waves on spherical surfaces

  1989cited by this paper
• Cyclic AMP waves during aggregation of Dictyostelium amoebae.

  1989cited by this paper
• The dynamics of three-dimensional scroll waves in excitable media

  1988cited by this paper
• Mechanism of Ventricular Vulnerability to Single Premature Stimuli in Open‐Chest Dogs

  1988cited by this paper
• The Motion of Untwisted Untorted Scroll Waves in Belousov-Zhabotinsky Reagent

  1988cited by this paper
• Chemical vortex dynamics in three-dimensional excitable media

  1988cited by this paper
• Simulation of wave‐propagation in three dimensions using fortran on the CYBER 205

  1988cited by this paper
• Singular perturbation theory of traveling waves in excitable media (a review)

  1988cited by this paper
• A computational study of twisted linked scroll waves in excitable media

  1987cited by this paper
• Two regimes of the scroll ring drift in the three-dimensional active media

  1987cited by this paper
• Twisted scroll waves in active three-dimensional media

  1985cited by this paper
• The Structure of the Core of the Spiral Wave in the Belousov-Zhabotinskii Reaction

  1985cited by this paper
• Dynamical simulations of twisted scroll rings in three-dimensional excitable media

  1985cited by this paper
• Organizing centres for three-dimensional chemical waves

  1984cited by this paper
• Chemical waves

  1984cited by this paper
• Singular filaments organize chemical waves in three dimensions

  1983cited by this paper
• Singular filaments organize chemical waves in three dimensions: I. Geometrically simple waves

  1983cited by this paper
• Singular filaments organize chemical waves in three dimensions: III. Knotted waves

  1983cited by this paper
• Computer Simulations of the Belousov-Zhabotinsky Reaction

  1983cited by this paper
• Three-dimensional chemical waves in the Belousov–Zhabotinskii reaction

  1983cited by this paper
• Adenosine 3',5'-monophosphate waves in Dictyostelium discoideum: a demonstration by isotope dilution--fluorography.

  1981cited by this paper
• Target patterns in a realistic model of the Belousov–Zhabotinskii reaction

  1980cited by this paper
• Elements of soliton theory

  1980cited by this paper
• Linear and Nonlinear Waves. By G. B. WHITHAM. Wiley-Interscience, 1974. 636 pp. $625.75

  1978cited by this paper
• Algebraic Topology: An Introduction

  1977cited by this paper
• Dictyostelium discoideum

  1975cited by this paper
• Two kinds of wave in an oscillating chemical solution

  1974cited by this paper
• Spiral Waves of Chemical Activity

  1972cited by this paper
• Impulses and Physiological States in Theoretical Models of Nerve Membrane.

  1961cited by this paper

• Strings, Branes and Twistons: Topological Analysis of Phase Defects in Excitable Media Such as the Heart.

  2024cites this paper
• Resonant drift of three-dimensional scroll rings in periodically forced reaction-diffusion systems

  2024cites this paper
• On concentric fractal spheres and spiral shells

  2024cites this paper
• Numerical study of the drift of scroll waves by optical feedback in cardiac tissue.

  2023cites this paper
• Scroll Waves and Filaments in Excitable Media of Higher Spatial Dimension.

  2023cites this paper
• Translating solutions of a generalized mean curvature flow in a cylinder: I. Constant boundary angles

  2022cites this paper
• From the Belousov-Zhabotinsky reaction to biochemical clocks, traveling waves and cell cycle regulation.

  2022cites this paper
• Spiral-generation mechanism in the two-dimensional FitzHugh-Nagumo system

  2022influential citation
• Mitotic Cycle Regulation. II. Traveling Waves

  2021cites this paper
• Hyperscroll dynamics: Vortices in four-dimensional networks.

  2021cites this paper
• Rotating spirals in oscillatory media with nonlocal interactions and their normal form

  2021cites this paper
• High-frequency pacing of scroll waves in a three-dimensional slab model of cardiac tissue.

  2021cites this paper
• Spiral Waves: Linear and Nonlinear Theory

  2020cites this paper
• Reconnection of multiple scroll rings in a three-dimensional reaction-diffusion system.

  2019cites this paper
• Simultaneous unpinning of multiple vortices in two-dimensional excitable media.

  2019cites this paper
• Unpinning of scroll waves attached to multiple heterogeneities

  2018cites this paper
• Stable and unstable vortex knots in excitable media.

  2018cites this paper
• Resonance of scroll rings with periodic external fields in excitable media.

  2018cites this paper
• New concepts for use in low-energy cardiac defibrillation

  2017cites this paper
• Chapter 17 Vortices Termination in the Cardiac Muscle

  2017cites this paper
• Dynamical behaviors of scroll rings in the presence of a dc electric field

  2017cites this paper
• Vortices Termination in the Cardiac Muscle

  2017cites this paper
• Effect of Surface Roughness on the Magnetic Field Profile in the Meissner State of a Superconductor

  2016cites this paper
• Local heterogeneities in cardiac systems suppress turbulence by generating multi-armed rotors

  2016cites this paper
• Effect of Tissue Structure (and) Disease on Simulated Arrhythmias in the Human Heart

  2016cites this paper
• Elastic Sheets, Phase Surfaces, and Pattern Universes

  2016cites this paper
• Dynamics of wave fronts and filaments in anisotropic cardiac tissue

  2015cites this paper
• A new far-field cardiac defibrillation mechanism

  2015cites this paper
• Scroll wave drift along steps, troughs, and corners.

  2015cites this paper
• Chemical waves in heterogeneous media.

  2014cites this paper
• Nonlinear and Stochastic Dynamics in the Heart.

  2014cites this paper
• Spatial confinement causes lifetime enhancement and expansion of vortex rings with positive filament tension

  2014cites this paper
• Effective dynamics of twisted and curved scroll waves using virtual filaments.

  2013cites this paper
• Interaction of a pair of parallel scroll waves.

  2013cites this paper
• 34 – Theory of Rotors and Arrhythmias

  2013cites this paper
• Scroll wave filaments self-wrap around unexcitable heterogeneities.

  2012cites this paper
• The structure of the quiescent core in rigidly rotating spirals in a class of excitable systems

  2012cites this paper
• Effects of reduced discrete coupling on filament tension in excitable media.

  2011cites this paper
• reentry in a 3D bidomain model Dynamics of virtual electrode-induced scroll-wave

  2011cites this paper
• Topologically Mismatched Pinning of Scroll Waves

  2011cites this paper
• Steady motion of hairpin-shaped vortex filaments in excitable systems.

  2010cites this paper
• A geometric theory for scroll wave filaments in anisotropic excitable media

  2009cites this paper
• Low-Energy Defibrillation Using Resonant Drift Pacing

  2009cites this paper
• Dynamics of Patterns in Nonlinear Equivariant PDEs

  2009cites this paper
• Equations for the membrane potential

  2009cites this paper
• Visualization of spiral and scroll waves in simulated and experimental cardiac tissue

  2008cites this paper
• Nonlinear dynamics of elastic filaments conveying a fluid and numerical applications to the static Kirchhoff equations

  2008cites this paper
• Dynamics of a transmural scroll wave in ground squirrel myocardium

  2007cites this paper
• Topological Constraints on Scroll and Spiral Waves in Excitable Media

  2007cites this paper
• Spiral wave dynamics: reaction and diffusion versus kinematics

  2006cites this paper
• Phase singularities and filaments: simplifying complexity in computational models of ventricular fibrillation.

  2006cites this paper
• Rotating spirals of curvature flows: a center manifold approach

  2005cites this paper
• Scroll waves meandering in a model of an excitable medium.

  2005cites this paper
• Curvature relation of wave front and wave changing in external field

  2005cites this paper
• Scroll Waves in Three Dimensions

  2004cites this paper
• Dynamics of virtual electrode-induced scroll-wave reentry in a 3D bidomain model.

  2004cites this paper
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  2004cites this paper
• Excitability in a model with a saddle-node homoclinic bifurcation

  2004cites this paper
• Activation Dynamics in Anisotropic Cardiac Tissue via Decoupling

  2004cites this paper
• Self-similar solutions for the kinematic model equation of spiral waves

  2004cites this paper
• Interaction dynamics of a pair of vortex filament rings.

  2003cites this paper
• Spiral waves in three-dimensional excitable media with light-sensitive reaction

  2003cites this paper
• Dynamics and Interaction of Filaments during reentry and Fibrillation in mammalian Virtual Ventricular Tissue

  2003cites this paper
• Equilibration of scroll Wave Filaments in the Ventricular Wall and the Minimal Principle

  2003cites this paper
• Spatio-Temporal Dynamics of Reaction-Diffusion Patterns

  2003cites this paper
• Isothermic Surfaces. The Calapso and Zoomeron Equations

  2002cites this paper
• Minimal principle for rotor filaments

  2002cites this paper
• Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity.

  2002cites this paper
• An analytical study of the physiology and pathology of the propagation of cardiac action potentials.

  2002cites this paper
• Dynamics and interaction of filaments in a computational model of re-entrant ventricular fibrillation.

  2002cites this paper
• A method to quantify the dynamics and complexity of re-entry in computational models of ventricular fibrillation

  2002cites this paper
• Large-excitability asymptotics for scroll waves in three-dimensional excitable media.

  2002cites this paper
• Motion by curvature of a three-dimensional filament: similarity solutions

  2002cites this paper
• Bäcklund and Darboux Transformations: Preface

  2002cites this paper
• Bäcklund and Darboux Transformations: CC-Ideals

  2002cites this paper
• Bäcklund and Darboux Transformations: Bäcklund Transformation and Darboux Matrix Connections

  2002cites this paper
• Bäcklund and Darboux Transformations: Tzitzeica Surfaces. Conjugate Nets and the Toda Lattice Scheme

  2002cites this paper
• Bäcklund and Darboux Transformations: General Introduction and Outline

  2002cites this paper
• Bäcklund and Darboux Transformations: Pseudospherical Surfaces and the Classical Bäcklund Transformation. The Bianchi System

  2002cites this paper
• Bäcklund and Darboux Transformations: The su (2)– so (3) Isomorphism

  2002cites this paper
• Bäcklund and Darboux Transformations: Biographies

  2002cites this paper
• Bäcklund and Darboux Transformations: Geometry and Modern Applications in Soliton Theory

  2002cites this paper
• Bäcklund and Darboux Transformations: General Aspects of Soliton Surfaces. Role of Gauge and Reciprocal Transformations

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  2002cites this paper
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  2002cites this paper
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• Cellular Automata and Lattice Boltzmann Techniques: an Approach to Model and Simulate Complex Systems

  2002cites this paper
• Dynamics and interaction of filaments in a computational model of re-entrant ventricular fibrillation

  2002cites this paper
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  2001cites this paper
• Diffusion-Generated Motion by Mean Curvature for Filaments

  2001cites this paper
• Explicit representation of planar wave speed and dispersive relation in general excitable media

  2000cites this paper
• Scroll wave dynamics in a three-dimensional cardiac tissue model: roles of restitution, thickness, and fiber rotation.

  2000cites this paper
• Complex chemical reactions — A review

  2000cites this paper
• Computer Modeling in Cardiac Electrophysiology

  2000cites this paper
• The motion of organization center of scroll waves in excitable media with single diffusion

  1999cites this paper
• Cellular automata modeling of physical systems

  1999cites this paper
• Interactions of spiral waves in inhomogeneous excitable media

  1998cites this paper
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  1998cites this paper