Spatially Discrete FitzHugh--Nagumo Equations

An improved pseudospectral approximation of generalized Burger-Huxley and Fitzhugh-Nagumo equations

In this research paper, an improved Chebyshev-Gauss-Lobatto pseudospectral approximation of nonlinear Burger-Huxley and Fitzhugh- Nagumo equations have been presented. The method employs chebyshev Gauss-Labatto points in time and space to obtain spectral accuracy. The mapping has introduced and transformed the initial-boundary value non-homogeneous problem to homogeneous problem. The main probl...

Pulse Propagation in Discrete Systems of Coupled Excitable Cells

Propagation of pulses in myelinated fibers may be described by appropriate solutions of spatially discrete FitzHugh-Nagumo systems. In these systems, propagation failure may occur if either the coupling between nodes is not strong enough or the recovery is too fast. We give an asymptotic construction of pulses for spatially discrete FitzHugh-Nagumo systems which agrees well with numerical simul...

Qualitative Theory of the FitzHugh-Nagumo Equations

Canonical reduction of self-dual Yang–Mills equations to Fitzhugh–Nagumo equation and exact solutions

The (constrained) canonical reduction of four-dimensional self-dual Yang–Mills theory to two-dimensional Fitzhugh–Nagumo and the real Newell–Whitehead equations are considered. On the other hand, other methods and transformations are developed to obtain exact solutions for the original two-dimensional Fitzhugh–Nagumo and Newell– Whitehead equations. The corresponding gauge potential Al and the ...

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...