(1 Consider the interaction of two species of animals in a habitat. We are told that the change of the populations x(t) and y(t) can be modeled by the quations For this system, the smaller eigenvalue is dx dt dy dt = 0.8x + 2y, = 3x + 2.22044604925031e - 16y. and the larger eigenvalue is
(1 Consider the interaction of two species of animals in a habitat. We are told that the change of the populations x(t) and y(t) can be modeled by the quations For this system, the smaller eigenvalue is dx dt dy dt = 0.8x + 2y, = 3x + 2.22044604925031e - 16y. and the larger eigenvalue is
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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![(1
Consider the interaction of two species of animals in a habitat. We are told that the change of the populations x(t) and y(t) can be modeled by
the quations
For this system, the smaller eigenvalue is
Symbiosis
dx
dt
dy
dt
= 0.8x + 2y,
=
1. What kind of interaction do we observe?
3x + 2.22044604925031e 16y.
and the larger eigenvalue is
[Note-- you may want to view a phase plane plot (right click to open in a new window).]
If y = Ay is a differential equation, how would the solution curves behave?
A. All of the solutions curves would converge towards 0. (Stable node)
B. All of the solution curves would run away from 0. (Unstable node)
C. The solution curves would race towards zero and then veer away towards infinity. (Saddle)
OD. The solution curves converge to different points.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0013f8ba-f182-49c6-a60e-512c0b337265%2F588e571f-8561-4f55-ac96-7df7e9290976%2Fgi3chvm_processed.png&w=3840&q=75)
Transcribed Image Text:(1
Consider the interaction of two species of animals in a habitat. We are told that the change of the populations x(t) and y(t) can be modeled by
the quations
For this system, the smaller eigenvalue is
Symbiosis
dx
dt
dy
dt
= 0.8x + 2y,
=
1. What kind of interaction do we observe?
3x + 2.22044604925031e 16y.
and the larger eigenvalue is
[Note-- you may want to view a phase plane plot (right click to open in a new window).]
If y = Ay is a differential equation, how would the solution curves behave?
A. All of the solutions curves would converge towards 0. (Stable node)
B. All of the solution curves would run away from 0. (Unstable node)
C. The solution curves would race towards zero and then veer away towards infinity. (Saddle)
OD. The solution curves converge to different points.
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