34. Consider the competition equations dz x+y a 1- I, dt K dy x+y b1- Y- dt Ky Here, x and y are populations that are in competition with each other. For the following parts, assume that (0) = = 750, y(0) = 500, a = b = 2, K 800, and Ky = 600. (a) Find the equilibria of the model. (b) Plot a phase plane diagram, indicating the equilibria, nullclines, and direction of growth across the nullclines. (c) Use Euler's method to approximate x and y for 010. Include a plot of x and y against t. Also include a phase-plane trajectory. (d) Describe what a and b represent for this model. Explain your reasoning. (e) Describe what K. and K. represent for this model. Explain your reasoning
34. Consider the competition equations dz x+y a 1- I, dt K dy x+y b1- Y- dt Ky Here, x and y are populations that are in competition with each other. For the following parts, assume that (0) = = 750, y(0) = 500, a = b = 2, K 800, and Ky = 600. (a) Find the equilibria of the model. (b) Plot a phase plane diagram, indicating the equilibria, nullclines, and direction of growth across the nullclines. (c) Use Euler's method to approximate x and y for 010. Include a plot of x and y against t. Also include a phase-plane trajectory. (d) Describe what a and b represent for this model. Explain your reasoning. (e) Describe what K. and K. represent for this model. Explain your reasoning
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:34. Consider the competition equations
dz
x+y
a 1-
I,
dt
K
dy
x+y
b1-
Y-
dt
Ky
Here, x and y are populations that are in competition with each other. For the following parts, assume
that (0) = = 750, y(0) = 500, a = b = 2, K 800, and Ky
= 600.
(a) Find the equilibria of the model.
(b) Plot a phase plane diagram, indicating the equilibria, nullclines, and direction of growth across
the nullclines.
(c) Use Euler's method to approximate x and y for 010. Include a plot of x and y against t.
Also include a phase-plane trajectory.
(d) Describe what a and b represent for this model. Explain your reasoning.
(e) Describe what K. and K. represent for this model. Explain your reasoning
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