Lotka-Volterra Predator-Prey

Lotka 1925, Volterra 1926 — Oscillating populations in phase space

Parameters

dx/dt = αx − βxy (prey)
dy/dt = δxy − γy (predator)
Equilibrium: x*=γ/δ, y*=α/β
Phase portrait: closed orbits.
Noise breaks orbits — real stochasticity.