Stochastic Lotka-Volterra

The deterministic Lotka-Volterra model has closed periodic orbits (neutrally stable). But demographic stochasticity (integer individuals, random births/deaths) causes trajectories to spiral outward and eventually go extinct. The Gillespie algorithm simulates exact stochastic dynamics: four reactions (prey birth, predation, predator birth, predator death) with exponentially distributed waiting times. Extinction time ~ exp(N) — rare but inevitable due to fluctuations. Compare to the deterministic (dashed) orbit.