FitzHugh–Nagumo Oscillator

Simplified neuron model with fast voltage variable v and slow recovery variable w. Shows excitability, limit cycles, and bifurcations.

Phase plane (v, w) with nullclines

Time series v(t) and w(t)

a (cubic shape) 0.70

b (w-nullcline slope) 0.80

τ (time scale ratio) 12.5

I_ext (applied current) 0.50

Actions

Model: dv/dt = v − v³/3 − w + I_ext; dw/dt = (v + a − bw)/τ. The v-nullcline is a cubic (fast); the w-nullcline is linear (slow). When they intersect on the unstable branch, a limit cycle exists (oscillatory neuron). "Pulse" injects a brief current stimulus to trigger a single action potential in excitable mode.