Rotating wave solutions of the FitzHugh-Nagumo equations.
This paper will treat the bifurcation and numerical simulation of rotating wave (RW) solutions of the FitzHugh-Nagumo (FHN) equations. These equations are often used as a simple mathematical model of excitable media. The dependence of the solutions on a uniformly applied current, and also on the diffusion coefficients or domain size will be studied. Ranges of applied current and/or diffusion coefficients in which RW solutions are observed will be described using bifurcation theory and continuation methods. The bifurcation of time-periodic solutions of these FHN equations without diffusion is described first. Similar methods are then used to find RW solutions on a circular ring and numerical simulations are described. These results are then extended to investigate RW solutions on annular rings of finite cross-section. Scaling arguments are used to show how the existence of solutions depends on either the diffusion coefficient or on the size of the region.
Alford
John G
JG
Department of Mathematics, Tulane University, New Orleans, LA 70118, USA. jalford@math.tulane.edu
Auchmuty
Giles
G
D000200:Action Potentials / Q000502:physiology; D002468:Cell Physiological Phenomena; D003198:Computer Simulation; D006801:Humans; D008432:Mathematical Computing; D008955:Models, Cardiovascular; D008959:Models, Neurological; D008962:Models, Theoretical; D017180:Tachycardia, Ventricular / Q000503:physiopathology