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?

Show your work to earn credit! Due on Thursday, February 1, 2024. 1. Let N(t) be the size of a population of fish. Assume this population grows 0 gistically and that the fish are harvested at the constant rate h, dtdN=f(N)h=rN(1KN)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