Electrical Waves in a One-Dimensional Model of Cardiac Tissue

DOI10.1137/070709980zbMath1167.34364OpenAlexW2116643462MaRDI QIDQ3624495

Christopher K. R. T. Jones, Margaret Beck, David G. Schaeffer, Martin Wechselberger

Publication date: 30 April 2009

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/6cadddfaea1bcb8a03084a429c888e0296384b92

zbMATH Keywords

blow-upgeometric singular perturbation theoryevans functionarrhythmiaalternanscardiac model

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) Estimates of eigenvalues in context of PDEs (35P15) Physiology (general) (92C30) Stability problems for infinite-dimensional dissipative dynamical systems (37L15) Singular perturbations for ordinary differential equations (34E15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Boundary value problems on infinite intervals for ordinary differential equations (34B40)

Related Items

One-dimensional reaction-diffusion dynamics in spatially bounded domains ⋮ Geometric desingularization of degenerate singularities in the presence of fast rotation: A new proof of known results for slow passage through Hopf bifurcations ⋮ Stability of traveling pulses with oscillatory tails in the FitzHugh-Nagumo system ⋮ Fast Pulses with Oscillatory Tails in the FitzHugh--Nagumo System ⋮ Shape reconstruction of cardiac ischemia from non-contact intracardiac recordings: a model study ⋮ Simple and multiple traveling waves in a reaction-diffusion-mechanics model ⋮ Existence and stability of traveling pulses in a reaction-diffusion-mechanics system ⋮ Do calcium buffers always slow down the propagation of calcium waves? ⋮ Traveling pulses and their bifurcation in a diffusive Rosenzweig-MacArthur system with a small parameter ⋮ Reversible signal transmission in an active mechanical metamaterial ⋮ Existence of Chapman--Jouguet Detonation and Deflagration Waves ⋮ Near-pulse solutions of the FitzHugh-Nagumo equations on cylindrical surfaces ⋮ Reduced models of cardiomyocytes excitability: comparing Karma and FitzHugh-Nagumo ⋮ Stable planar vegetation stripe patterns on sloped terrain in dryland ecosystems ⋮ Stability of traveling wave in a PDE approximation of coupled arrays of Chua's circuit ⋮ Shock-fronted travelling waves in a reaction-diffusion model with nonlinear forward-backward-forward diffusion