Three-dimensional waves in excitable reaction-diffusion systems

DOI10.1007/BF00275497zbMath0646.92002WikidataQ113909314 ScholiaQ113909314MaRDI QIDQ1104259

Jagannathan Gomatam, Peter Grindrod

Publication date: 1987

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

zbMATH Keywords

spheretorusexcitable mediaeikonal equationclosed orientable surfacethree-dimensional wavesgeometrical stabilityexcitable reaction- diffusion systemsexistence and propagation of rotationally symmetric and double spiral wavesexpanding spherehelical wavenon-uniform rate of rotation of cross-sectional spiral wavestoroidal and twisted toroidal scroll waves

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) General biology and biomathematics (92B05)

Related Items

The eikonal approximation to excitable reaction-diffusion systems: travelling non-planar wave fronts on the plane, Singular perturbation theory of traveling waves in excitable media (A review), A plausible mechanism for the motion of untwisted scroll rings in excitable media, Diversity of three-dimensional chemical waves, One-way blocks in cardiac tissue: A mechanism for propagation failure in Purkinje fibres, Spiral waves on static and moving spherical domains, Mathematical modeling of the excitation process in myocardial tissue: Influence of fiber rotation on wavefront propagation and potential field, Spreading of excitation in 3-D models of the anisotropic cardiac tissues. I: Validation of the eikonal model, Reaction-diffusion waves in the vicinity of obstacles: the eikonal approach, One-way blocks in excitable media, Diffraction of reaction-diffusion waves: the conformal-mapped eikonal equation, Wavefront propagation in an activation model of the anisotropic cardiac tissue: Asymptotic analysis and numerical simulations

Cites Work

• The geometry and motion of reaction-diffusion waves on closed two- dimensional manifolds
• Pattern synthesis from singular solutions in the Debye limit: helical waves and twisted toroidal scroll structures
• A Geometrical Theory for Spiral Waves in Excitable Media
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