Question
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
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?
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