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
