Leaky integrate-and-fire neuron with synaptic input and noise. Watch membrane potential integrate to threshold, spike, and reset. Inter-spike interval histogram reveals Poisson vs regular firing.
The leaky integrate-and-fire (LIF) model: τ_m dV/dt = -V + R·I + σ·ξ(t). When V reaches threshold Vth=1, a spike is emitted and V resets to 0. The ISI distribution is the first-passage time distribution of an Ornstein-Uhlenbeck process — transitions from regular (low noise) to Poisson-like (high noise) firing.