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d. What happens if P < M for all t?

d. What happens if P < M for all t?

Advanced Engineering Mathematics
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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solve part d

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?
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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