Lake eutrophication — catastrophic regime shift with hysteresis
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.