The FitzHugh-Nagumo (FHN) model

A generalisation of the Van der Pol's equation the FHN is one of the simplest model for excitable media [1,2]. The model is able to reproduce many qualitative characteristics of electrical impulses in cardiac tissues, e.g.: 1D travelling waves, tip of 2D spirals meandering, instability of 3D spiral wave with negative tension, oscillating pacemakers.

The FHN system of equations for one cell

    du/dt = F(u, v) = u(1 - u)(u - a) - v,
    dv/dt = H(u, v) = ε (bu - v),

where a is the threshold for excitation. To the right below u(t) excitation (black) and v(t) recovery (blue) variables are plotted. To the left the (u, v) phase plane of the system is shown. F(u,v) = 0 null cline is the red line and H(u,v) = 0 null cline is the green line.

Below you can explore the model for different parameter values. The script makes 800 time steps dt.
a b ε

dt u0 v0 Ymin Ymax field
The system makes excitation cycle and goes to the stable fixed point (u=0, v=0). Note that for small ε values the excitation variable u is fast with abrupt steps and the recovery v is slow.

[1] FitzHugh-Nagumo model in Scholarpedia
[2] J.D. Murray Mathematical Biology I. An Introduction

Heart rhythms     updated 29 Nov 2011