Scroll waves in isotropic excitable media: Linear instabilities, bifurcations, and restabilized states

DOI10.1103/PhysRevE.65.046235zbMath1244.35071arXivcond-mat/0201467WikidataQ74077346 ScholiaQ74077346MaRDI QIDQ2903441

Vincent Hakim, H. Henry

Publication date: 9 August 2012

Published in: Physical Review E (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/cond-mat/0201467

zbMATH Keywords

scroll wavesisotropic excitable media

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Bifurcations in context of PDEs (35B32)

Related Items (9)

A geometric theory for scroll wave filaments in anisotropic 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 ⋮ Exact coherent structures and chaotic dynamics in a model of cardiac tissue ⋮ Adjoint eigenfunctions of temporally recurrent single-spiral solutions in a simple model of atrial fibrillation ⋮ (INVITED) Reaction-diffusion waves in cardiovascular diseases ⋮ Three-dimensional lattice Boltzmann model for the complex Ginzburg-Landau equation ⋮ A theory for spiral wave drift in reaction-diffusion-mechanics systems ⋮ Negative filament tension in the Luo-Rudy model of cardiac tissue

Cites Work

• The dynamics of scroll wave filaments in the complex Ginzburg-Landau equation
• The dynamics of three-dimensional scroll waves in excitable media
• An efficient method for computing leading eigenvalues and eigenvectors of large asymmetric matrices
• DNA and differential geometry
• Helical organizing centers in excitable media
• Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation
• Filament instability and rotational tissue anisotropy: A numerical study using detailed cardiac models
• Decomposition of the linking number of a closed ribbon: A problem from molecular biology
• Varieties of spiral wave behavior: An experimentalist’s approach to the theory of excitable media
• Fast Simulations of Waves in Three-Dimensional Excitable Media
• Self-Linking and the Gauss Integral in Higher Dimensions
• Tension of organizing filaments of scroll waves

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