Mathematics Question...?

[louisa.mcbreen]

Levins suggested modeling not the number of individuals but the fraction of patches that a population occupies. He suggested the following equation:
P' = cP(h - P) - P,
where P(t) denotes the fraction of occupied patches. The number h denotes the fraction of patches that is actually habitable for the population and, hence, h - P is the number of empty but habitable patches. Note that 0 P h 1. The population colonizes empty patches with rate c. Occupied patches become empty with rate .

a) Find the steady states of the system.

b) Assume that h can be varied (e.g. construction takes up habitable patches). Draw the bifurcation diagram with h as the parameter. Do all the habitable patches have to be destroyed before the population dies out?

Regarding part a), I have found the steady states to be P=0 or P=h-(/c), which I believe are correct.
I am having quite a bit of trouble with part b) though. Some help/guidance would be much appreciated!
Thanks.