Stochastic Lotka-Volterra & Extinction Risk — The deterministic LV system dx/dt = αx−βxy, dy/dt = δxy−γy has a center (neutrally stable cycles). Adding demographic noise (SDE: dXₜ = f·dt + σ√X·dWₜ) destroys this structure — trajectories spiral outward and hit the extinction boundary. The mean extinction time T_ext scales as exp(N·φ) where N is population size and φ is an action (Hamiltonian path integral). Phase portrait shows all trajectories; time series below tracks ensemble evolution.