The dynamics of three-dimensional scroll waves in excitable media

DOI10.1016/0167-2789(88)90080-2zbMath0645.76052OpenAlexW2037157420MaRDI QIDQ1103466

James P. Keener

Publication date: 1988

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(88)90080-2

zbMATH Keywords

perturbation theoryscroll waveexcitable mediummultiscale techniquescentral filamenttwist of the scroll wavetwo-dimensional spiral solutions

Mathematics Subject Classification ID

Absolute and convective instability and stability in hydrodynamic stability (76E15)

Related Items (45)

Dynamics of wave fronts in excitable media ⋮ Stationary self-propagating fronts in potential flow ⋮ Anchoring of vortex filaments in 3D excitable media ⋮ Scroll waves in isotropic excitable media: Linear instabilities, bifurcations, and restabilized states ⋮ IDENTIFICATION OF EXCITABLE MEDIA USING CELLULAR AUTOMATA MODELS ⋮ Helical and circular scroll wave filaments ⋮ Drift of scroll waves of electrical excitation in an isotropic model of the cardiac left ventricle ⋮ A geometric theory for scroll wave filaments in anisotropic excitable media ⋮ Singular perturbation theory of traveling waves in excitable media (A review) ⋮ Evolution of twist of an autowave vortex ⋮ Spiral waves of cyclic AMP in a model of slime mold aggregation ⋮ Dynamical stability of untwisted scroll rings in excitable media ⋮ Negative tension of scroll wave filaments and turbulence in three-dimensional excitable media and application in cardiac dynamics ⋮ LOCALIZATION OF RESPONSE FUNCTIONS OF SPIRAL WAVES IN THE FITZHUGH–NAGUMO SYSTEM ⋮ Rotating spirals in oscillatory media with nonlocal interactions and their normal form ⋮ Rings on strings in excitable media ⋮ Adjoint eigenfunctions of temporally recurrent single-spiral solutions in a simple model of atrial fibrillation ⋮ Knotted scroll wave filaments in excitable media ⋮ Spiral wave dynamics in excitable media with spherical geometries ⋮ Stable three-dimensional action potential circulation in the FitzHugh- Nagumo model ⋮ Dynamics of linked filaments in excitable media ⋮ A cellular automaton model of excitable media. II: Curvature, dispersion, rotating waves and meandering waves ⋮ A cellular automaton model of excitable media. III: Fitting the Belousov- Zhabotinskii reaction ⋮ (INVITED) Reaction-diffusion waves in cardiovascular diseases ⋮ A theory for spiral wave drift in reaction-diffusion-mechanics systems ⋮ A cellular automaton model of excitable media. IV: Untwisted scroll rings ⋮ Spiral wave solutions for reaction-diffusion equations in a fast reaction/slow diffusion limit ⋮ The dynamics of helical scroll waves in excitable media ⋮ The motion of organization center of scroll waves in excitable media with single diffusion ⋮ Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation ⋮ Reentrant waves and their elimination in a model of mammalian ventricular tissue ⋮ Scroll waves in spherical shell geometries ⋮ Cookbook asymptotics for spiral and scroll waves in excitable media ⋮ Response Functions of Spiral Wave Solutions of the Complex GinzburgLandau Equation ⋮ Induced drift of scroll waves in the Aliev-Panfilov model and in an axisymmetric heart left ventricle ⋮ Lie symmetry analysis for classification on pattern in excitable media ⋮ The dynamics of scroll wave filaments in the complex Ginzburg-Landau equation ⋮ Three-dimensional reconstruction of organizing centers in excitable chemical media ⋮ Autowave propagation for general reaction diffusion systems ⋮ Interactions of spiral waves in inhomogeneous excitable media ⋮ Robust data assimilation with noise: Applications to cardiac dynamics ⋮ Knotted vortex filaments in an ideal fluid ⋮ Minimal surface generating flow for space curves of non-vanishing torsion ⋮ Structure of wave front and organization center in excitable media ⋮ Computational study of helix wave formation in active media

Cites Work

• A computational study of twisted linked scroll waves in excitable media
• Singular perturbation theory of traveling waves in excitable media (A review)
• Perturbation methods in applied mathematics
• Target pattern and spiral solutions to reaction-diffusion equations with more than one space dimension
• The Motion of Untwisted Untorted Scroll Waves in Belousov-Zhabotinsky Reagent
• A Green’s function for a linear equation associated with solitons
• Spiral Waves in Reaction-Diffusion Equations

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