Stochastic Theta Neuron — Excitability

dθ/dt = 1−cos(θ) + (1+cos(θ))·[I+η(t)]: SNIPER bifurcation, ISI statistics

I=−0.30
The theta neuron is the normal form of the SNIPER (saddle-node on invariant circle) bifurcation — the canonical Type I excitability. Below threshold (I<0): quiescent; above (I>0): periodic firing. Noise induces stochastic spiking below threshold; ISI distribution transitions from exponential to peaked near-periodic at strong drive.