4. A model for the population of pigeons in the United States is given by the autonomous DE: Р3 (1— Р)(1 - 2Р)P. To answer the following questions you do not need to solve the DE. points] (a) Find the critical points and phase portrait of the DE. (Portraits without a proper justification for the arrows will get zero credit.) (b) Classify each critical point as asymptotically stable, unstable or semi-stable. (c) Sketch typical solution curves in the regions (in the xy- plane) determined by the graphs of equilibrium solutions.
4. A model for the population of pigeons in the United States is given by the autonomous DE: Р3 (1— Р)(1 - 2Р)P. To answer the following questions you do not need to solve the DE. points] (a) Find the critical points and phase portrait of the DE. (Portraits without a proper justification for the arrows will get zero credit.) (b) Classify each critical point as asymptotically stable, unstable or semi-stable. (c) Sketch typical solution curves in the regions (in the xy- plane) determined by the graphs of equilibrium solutions.
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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![4. A model for the population of pigeons in the United States is given by
the autonomous DE:
Р - (1 — Р)(1 — 2P)P.
To answer the following questions you do not need to solve the DE.
points]
(a) Find the critical points and phase portrait of the DE. (Portraits
without a proper justification for the arrows will get zero credit.)
(b) Classify each critical point as asymptotically stable, unstable or
semi-stable.
(c) Sketch typical solution curves in the regions (in the xy, plane)
determined by the graphs of equilibrium solutions.
(d) Let P(t) denotes the pigeon population in thousands and P(0) = Po
be the initial pigeon population. What is the range of values for Po
so that the pigeon population thrives in the long term.
(e) Does the Pigeon population become extinct in finite time? Justify
your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4e4c829-f598-4523-ba66-76332cdb1366%2F2800402f-fe36-4a3b-a510-b5a81d90eed2%2Fjjs8pdm_processed.png&w=3840&q=75)
Transcribed Image Text:4. A model for the population of pigeons in the United States is given by
the autonomous DE:
Р - (1 — Р)(1 — 2P)P.
To answer the following questions you do not need to solve the DE.
points]
(a) Find the critical points and phase portrait of the DE. (Portraits
without a proper justification for the arrows will get zero credit.)
(b) Classify each critical point as asymptotically stable, unstable or
semi-stable.
(c) Sketch typical solution curves in the regions (in the xy, plane)
determined by the graphs of equilibrium solutions.
(d) Let P(t) denotes the pigeon population in thousands and P(0) = Po
be the initial pigeon population. What is the range of values for Po
so that the pigeon population thrives in the long term.
(e) Does the Pigeon population become extinct in finite time? Justify
your answer.
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