Question 12. population. The following differential equation describes the dynamics of a x' = x²(2-x) - hx, where h> 0 is the intensity of harvesting. (a) Find all equilibria. [Hint: some of them will depend on h.] (b) For which values of h is there at least one positive equilibrium? (c) For h = 5/9 determine the stability of each equilibrium analytically (not from the phase line diagram).
Question 12. population. The following differential equation describes the dynamics of a x' = x²(2-x) - hx, where h> 0 is the intensity of harvesting. (a) Find all equilibria. [Hint: some of them will depend on h.] (b) For which values of h is there at least one positive equilibrium? (c) For h = 5/9 determine the stability of each equilibrium analytically (not from the phase line diagram).
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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![Question 12.
population.
The following differential equation describes the dynamics of a
x = x²(2-x) - hx,
where h> 0 is the intensity of harvesting.
(a) Find all equilibria. [Hint: some of them will depend on h.]
(b) For which values of h is there at least one positive equilibrium?
(c) For h = 5/9 determine the stability of each equilibrium analytically (not from the phase
line diagram).
(d) For h = 5/9, sketch the phase-line diagram for 0 ≤ x ≤ 2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10d8e2b7-2a67-49c2-b661-a97dbb4b37a8%2F158d86a1-2998-44c2-8981-d277bda2ea31%2Fr6o8ojuj.png&w=3840&q=75)
Transcribed Image Text:Question 12.
population.
The following differential equation describes the dynamics of a
x = x²(2-x) - hx,
where h> 0 is the intensity of harvesting.
(a) Find all equilibria. [Hint: some of them will depend on h.]
(b) For which values of h is there at least one positive equilibrium?
(c) For h = 5/9 determine the stability of each equilibrium analytically (not from the phase
line diagram).
(d) For h = 5/9, sketch the phase-line diagram for 0 ≤ x ≤ 2.
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