Excitation and recovery waves in the simplified Hodgkin-Huxley nerve impulse model
dv/dt = v − v³/3 − w + I
dw/dt = ε(v + a − bw)
+D∂²v/∂x² (spatial coupling)
v = voltage-like activator (fast)
w = recovery variable (slow)
Below threshold: perturbations decay. Above threshold: excitation travels as a pulse with refractory tail. The phase plane shows the nullclines — stable limit cycle when I is large enough.