e. Discuss the solutions to the differential equation. What are the equilibrium points of the model? Explain the dependence of the steady- state value of P on the initial values of P. About how many permits should be issued?
e. Discuss the solutions to the differential equation. What are the equilibrium points of the model? Explain the dependence of the steady- state value of P on the initial values of P. About how many permits should be issued?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please solve the last part, e. Discuss the solutions to the differential equation. What are the equilibrium points of the model? Explain the dependence of the steady state value of P on the initial values of P. About how many permits should be issued?
Transcribed Image Text:The fish and game department in a certain state is planning
to issue hunting permits to control the deer population (one deer per
permit). It is known that if the deer population falls below a certain level m,
the deer will become extinct.
It is also known that if the deer population rises above the carrying capacity
M, the population will decrease back to M through disease and malnutrition.
a. Discuss the reasonableness of the following model for the growth rate
of the deer population as a function of time:
dP
=
=rP(M-P)(Pm)
dt
where P is the population of the deer and r is a positive constant of
proportionality. Include a phase line.
b. Explain how this model differs from the logistic model
dP
=rP(M-P)
dt
Is it better or worse than the logistic model?
c. What happens if P > M for all t?
d. What happens if P < M for all t?
e. Discuss the solutions to the differential equation. What are the
equilibrium points of the model? Explain the dependence of the steady-
state value of P on the initial values of P. About how many permits should
be issued?
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