Ecological Resilience & Fold Catastrophe
Alternative stable states, hysteresis, and tipping points in shallow lake ecosystems
Scheffer's lake model (1993): du/dt = r·P·u^n/(h^n+u^n) − h·u. Two stable states coexist (clear and turbid) for a range of nutrient loading P — alternative stable states. The system exhibits a fold catastrophe: past the tipping point, a sudden irreversible shift occurs (regime shift). Recovering the clear state requires reducing P far below the forward tipping point — hysteresis. Early warning signals (rising variance, slowing recovery) precede the tipping point.