Aliev-Panfilov model

The AP system of equations for one cell is
    du/dt = F(u, v) = ku(1 - u)(u - a) - uv,
    dv/dt = H(u, v) = ε(u)(ku - v),

where a = 0.05 is the threshold for excitation and parameter k = 8 controls the magnitude of the transmembrane current. ε(u) is a step function setting the time scale of the recovery: we set ε(u < 0.05) = 1 and ε(u > 0.05) = 0.1 . The term uv describes the repolarizing current of the recovery process.

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 k

dt u0 v0 Ymin Ymax field
The system makes excitation cycle and goes to the stable fixed point (u=0, v=0).

Heart rhythms     updated 9 June 2012