Trophic Cascade — Predator-Herbivore-Plant Dynamics

Tri-trophic Lotka-Volterra system: wolves (P), elk (H), and vegetation (V). Remove predators and watch the trophic cascade: herbivore explosion followed by vegetation collapse. Real ecosystem in phase space.

System Controls

dV/dt = rV(1-V/K) - aHV dH/dt = eₐaHV - dₕH - bPH·[pred] dP/dt = eᵦbPH - dₚP Trophic cascade: P↓ → H↑ → V↓ Stable limit cycle when all three coexist.