Extinction thresholds, bifurcations, and population dynamics
Logistic growth: dN/dt = rN(1−N/K) has a stable equilibrium at N=K and unstable at N=0.
The weak Allee effect reduces per-capita growth at low density but no extinction threshold.
The strong Allee effect: dN/dt = rN(N/A−1)(1−N/K) creates a bistable system —
populations above threshold A grow; below it they collapse. Adding harvesting shifts these thresholds,
causing saddle-node bifurcations and sudden extinction transitions.