Ecological Fold Bifurcation & Hysteresis

Lake eutrophication — catastrophic regime shift with hysteresis

Current state
Algae X:

Catastrophic Shifts

Lakes can switch abruptly from clear to turbid (algae-dominated) when nutrient loading crosses a threshold. Due to hysteresis, recovery requires reducing nutrients far below the tipping point — the system "remembers" its history. This is a classic fold (saddle-node) bifurcation.

Model: dX/dt = P + rX²/(X²+1) − hX (Scheffer 1997). Stable branches are solid; unstable dashed.