Show your work to earn credit! Due on Thursday, February 1, 2024.\ Let

N(t)

be the size of a population of fish. Assume this population grows logistically and that the fish are harvested at the constant rate

h

,\

(dN)/(dt)=f(N)-h=rN(1-(N)/(K))-h

\

K

is the carrying capacity,

r

is the intrinsic rate of growth, and

h

, the harvest rate, is a bifurcation parameter. Sketch the bifurcation diagram for this system. Be sure to identify the stability of each branch of your bifurcation diagram. For what value of

h

is there a bifurcation? What kind of bifurcation is this? Describe the long-term behavior of the fish population for harvest rates on either side of this bifurcation. Is there something wrong with this model?