تم الحل ✓
categoryرياضيات
schoolبكالوريوس
event_available2026-07-13
السؤال
Transcribed Image Text:
10. For a fish population modeled by a depensation growth model, we
have, when there is harvesting,
where
d
dt
N= F(N) H(N),
and H(N) = qEN.
F(N) N (N/N - 1)(1-N/K)
a. Find (and plot, freehand) the sustained yield H(3) as a function of
effort E, and the unsustainable yield H(N2), also as a function of E (and
plot on the same figure). Here №3 is the nontrivial stable equilibrium of
N and N is the unstable equilibrium.
b. Find the E (= Emax), where the two curves in (a) merge (this happens
when NN3). What happens to the fishery and the fish population when
E = Emax?
=
c. Suppose harvesting is done at effort level E = Emax for a while so that
the fish population is below what was thought of as the “sustainable” N
(which is equal to №2, so actually it is not really sustainable). Realizing
that there is a problem, the government puts in a fishing limit that
reduces the effort E to slightly below Emax. Can the fishery recover?
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