Stochastic Predator-Prey (Gillespie)

Demographic noise, extinction, and quasi-cycles via exact Gillespie simulation

α (prey birth): β (predation): γ (pred death): δ (pred grow):

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Exact Gillespie SSA (Stochastic Simulation Algorithm) for the Lotka-Volterra reaction network: X→2X (birth), X+Y→2Y (predation), Y→∅ (predator death), X+Y→X+2Y. Demographic noise drives the system off the deterministic orbit, causing quasi-cycles (spiral toward fixed point) and — at small populations — extinction events.