dS/dt = f(S) = kS(1-S/N)(S/M-1)

Question

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?