Consider our model of a fox squirrel population from the previous sec...

Consider our model

of a fox squirrel population from the previous section. Suppose that the parameters M and k remain relatively constant over the long term but as more people move into the area, the parameter N (the carrying capacity) decreases.

(a) Assuming that M ≤ N, sketch the graph of the function f (S) for fixed values of k and M and several values of N.

(b) At what value of N does a bifurcation occur?

(c) How does the population of fox squirrels behave if the parameter N slowly and continuously decreases toward the bifurcation value?