Ecological Bifurcation: Alternative Stable States

Shallow lakes switch between clear-water and turbid algal states via catastrophic fold bifurcation

Controls

Bifurcation
Dynamics
Lake View

Loading

0.50
1.00

Ecosystem

0.50
0.60

State

CLEAR WATER
Turbidity X
dX/dt

Model

Scheffer's lake model (1993): turbidity X has positive feedback via internal nutrient recycling — creates bistability and hysteresis.
dX/dt = L + r·X²/(h²+X²) - s·X
Two stable states coexist between fold points. Recovery requires L much lower than the forward tipping point — hysteresis!