Exercise 8.3.2: Suppose the hares do not grow exponentially, but logistically. In particular consider x' = (0.4 – 0.01 y)x – yx², y' = (0.003x – 0.3)y. %3D %3D For the following two values of y, find and classify all the critical points in the positive quadrant, that is, for x > 0 and y 2 0. Then sketch the phase diagram. Discuss the implication for the long term behavior of the population. a) y = 0.001, b) y = 0.01.
Exercise 8.3.2: Suppose the hares do not grow exponentially, but logistically. In particular consider x' = (0.4 – 0.01 y)x – yx², y' = (0.003x – 0.3)y. %3D %3D For the following two values of y, find and classify all the critical points in the positive quadrant, that is, for x > 0 and y 2 0. Then sketch the phase diagram. Discuss the implication for the long term behavior of the population. a) y = 0.001, b) y = 0.01.
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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Transcribed Image Text:Exercise 8.3.2: Suppose the hares do not grow exponentially, but logistically. In particular consider
x' = (0.4 – 0.01 y)x – yx²,
y' = (0.003x – 0.3)y.
|
For the following two values of y, find and classify all the critical points in the positive quadrant,
that is, for x > 0 and y > 0. Then sketch the phase diagram. Discuss the implication for the long
term behavior of the population.
a) y = 0.001,
b) y = 0.01.
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