Stability of travelling front solutions of the Fitzhugh-Nagumo equations

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 co...

Stability of Pulse Solutions for the Discrete FitzHugh–Nagumo System

We show that the fast travelling pulses of the discrete FitzHugh–Nagumo system in the weak-recovery regime are nonlinearly stable. The spectral conditions that need to be verified involve linear operators that are associated to functional differential equations of mixed type. Such equations are ill-posed and do not admit a semi-flow, which precludes the use of standard Evans-function techniques...

Qualitative Theory of the FitzHugh-Nagumo Equations

Spatially Discrete FitzHugh--Nagumo Equations

We consider pulse and front solutions to a spatially discrete FitzHugh–Nagumo equation that contains terms to represent both depolarization and hyperpolarization of the nerve axon. We demonstrate a technique for deriving candidate solutions for the McKean nonlinearity and present and apply solvability conditions necessary for existence. Our equation contains both spatially continuous and discre...

Stability of the Travelling Wave Solution of the Fitzhugh - Nagumo System

Travelling wave solutions for the FitzHugh-Nagumo equations have been proved to exist, by various authors, close to a certain singular limit of the equations. In this paper it is proved that these waves are stable relative to the full system of partial differential equations; that is, initial values near (in the sup norm) to the travelling wave lead to solutions that decay to some translate of ...