Exercise 5. (Fishery Model) The equation N = rN(1 –) – H represent a simple population model of a fishery with the term –H representing a constant harvesting rate (H > 0). a) Show that the system can be written in dimensionless form as dr = ¤(1–¤) – h dr for suitably defined dimensionless quantities.
Exercise 5. (Fishery Model) The equation N = rN(1 –) – H represent a simple population model of a fishery with the term –H representing a constant harvesting rate (H > 0). a) Show that the system can be written in dimensionless form as dr = ¤(1–¤) – h dr for suitably defined dimensionless quantities.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Exercise 5.
(Fishery Model) The equation N = rN(1 – ) – H represent a
K
simple population model of a fishery with the term -H representing a constant harvesting
rate (H > 0).
a) Show that the system can be written in dimensionless form as
dx
= #(1–2) – h
dT
for suitably defined dimensionless quantities.
b) Plot the vector fields for different values of h (show all qualitative behaviors).
c) Show that a bifurcation happens at a critical value he, determine the value, and classify
the bifurcation.
d) Discuss the long-time behavior of the population for h < he and h > he, and give a
biological interpretation to both cases.
e)
have explored. Determine what the flaw is and advance a possible solution. (Hint: it is
related to a missing fixed point)
This model has a major flaw compared to other population models we
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