Assume that m(p) = a + bp for some constants a,b > 0. That is, the extinction rate increases withp because of competition between subpopulations, but m(p) does not dp vanish as p→0. The model for proportion of occupied sites is = cp(1 - p) - (a + bp)p. Assuming that the subpopulations obey the differential equation and the cofficients are a = 4, b = 1, but c is allowed to take any value, complete parts (a) through (c). (a) Find the equilibrium values of p (your answer will depend on the unknown coefficient c). The equilibrium values are p = (Simplify your answer. Use a comma to separate answers as needed.)
Assume that m(p) = a + bp for some constants a,b > 0. That is, the extinction rate increases withp because of competition between subpopulations, but m(p) does not dp vanish as p→0. The model for proportion of occupied sites is = cp(1 - p) - (a + bp)p. Assuming that the subpopulations obey the differential equation and the cofficients are a = 4, b = 1, but c is allowed to take any value, complete parts (a) through (c). (a) Find the equilibrium values of p (your answer will depend on the unknown coefficient c). The equilibrium values are p = (Simplify your answer. Use a comma to separate answers as needed.)
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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8.2-3a)
Transcribed Image Text:Assume that m(p) = a + bp for some constants a,b>0. That is, the extinction rate increases withp because of competition between subpopulations, but m(p) does not
dp
vanish as p→0. The model for proportion of occupied sites is
dt
= cp(1 - p) - (a + bp)p. Assuming that the subpopulations obey the differential equation and the
coefficients are a = 4, b = 1, but c is allowed to take any value, complete parts (a) through (c).
(a) Find the equilibrium values of p (your answer will depend on the unknown coefficient c).
The equilibrium values are p=
(Simplify your answer. Use a comma to separate answers as needed.)
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