The model dx 4x – x? 4xy dt dy -y + 2y? dt describes two interacting species, x and y. Which of the following statements are TRUE and which are FALSE? Justify your answers! (You will need to sketch the phase diagram to answer some of the questions) (3.1) This is a predator-prey system, where y is the prey and x is the predator. (2 2) S peeies Dout

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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The model
dx
4x – x² – 4xy
dt
dy
= -y + 2y?
dt
describes two interacting species, x and y. Which of the following statements are TRUE and which
are FALSE? Justify your answers! (You will need to sketch the phase diagram to answer some of
the questions)
(3.1) This is a predator-prey system, where y is the prey and x is the predator.
(3.2) Species y can survive without species x.
(3.3) Species x can survive without species y.
(3.4) The two species are competing for the same resources.
(3.5) If the initial populations are large enough, both populations can grow without bound.
(3.6) Both populations will always die out.
Transcribed Image Text:The model dx 4x – x² – 4xy dt dy = -y + 2y? dt describes two interacting species, x and y. Which of the following statements are TRUE and which are FALSE? Justify your answers! (You will need to sketch the phase diagram to answer some of the questions) (3.1) This is a predator-prey system, where y is the prey and x is the predator. (3.2) Species y can survive without species x. (3.3) Species x can survive without species y. (3.4) The two species are competing for the same resources. (3.5) If the initial populations are large enough, both populations can grow without bound. (3.6) Both populations will always die out.
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