Suppose that there are 10 communities located around a single shared lake. Each community derives bene?ts from the resources of the lake (such as recreation and a source of water). However, each community also generates phosphorus pollution that enters the lake.

Let x be amount of phosphorus in the lake water and let ? x = f(x;a) be a di?erential equation that describes how the net ?ow of phosphorus into the lake water depends on x and a nonnegative parameter a corresponding to the total phosphorus pollution entering the lake from the communities. The function f for the case when a = 0 is shown in the ?gure below. An interactive model where you can adjust the value of a is posted on Desmos at https://www.desmos.com/calculator/g5l5tuccql

Phosphorus pollution is an interesting example of nonlinear ecosystem dynamics. I will provide some additional resources related to this problem on Canvas.

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