Figure 7: Lake Dynamics for b=0.48
Figure 8: Lake Dynamics for b=0.6
• 2 ≤ b ≤ 8 √3
For values of b in this range, a has three equilibria. (See Figure 8)
This is the hysteresis effect: the lake remains in an oligotrophic state
up to a certain point at which it flips to a eutrophic state. The point at
which the lake flips from oligotrophic to eutrophic is where da/dx = 0 at
(xF1, aF1) = (0.4084, 0.1021) and is an unstable steady-state. The point
(x, a) = (0.7876, 0.0897) is a stable eutrophic state. This hysteresis allows
eutrophication to be reversible, however, as lowering external loading be-
26
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