SNIPER Bifurcation

Saddle-Node Infinite-PERiod bifurcation: a fixed point collides with a limit cycle
Parameter I (current) 0.80
Noise σ 0.05
Damping b 1.00
Time Scale 1.0
State: ... Period: ... I_crit: ...
SNIPER (also SNIC): as parameter I increases past I_c, a saddle and stable node collide on a limit cycle, and the system transitions from rest to periodic firing. Period T ~ π/√(I-I_c) near the bifurcation — infinite period (DC firing rate = 0 at threshold). Common in neuroscience: Type I neurons (integrate-and-fire near threshold).