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15. Use a spreadsheet for this problem, and attach your results in your PDF submission. There is a template of a Google Sheets you may use in the Course Calendar, but the formulas do NOT reflect the ones below and you will have to adjust them. Consider the following model of competition between two species, P and Q: Pn+1 = Pn+rPn K₁-Pn-sQn K₁ K2-Qn-vPn K2 Qn+1 = Qn+uQn (a) When r = u = 1, s = 0.75, v = 0.50, K₁ = 1200 and K2 = 1000 the two species reach a non-zero equilibrium, meaning that the two populations can continue to coexist. Make a graph that illustrates the populations starting with initial populations of Po= 500 and Qo = 200 and approaching this equilibrium. (b) Find values of r, s, u and v such that species P dies out, and species Q approaches its carrying capacity K2. Write the values of r, s, u and v that you found, along with the initial population values that you used, on your paper. Include a graph that illustrates this behavior.

15. Use a spreadsheet for this problem, and attach your results in your PDF submission. There is a template of a Google Sheets you may use in the Course Calendar, but the formulas do NOT reflect the ones below and you will have to adjust them. Consider the following model of competition between two species, P and Q: Pn+1 = Pn+rPn K₁-Pn-sQn K₁ K2-Qn-vPn K2 Qn+1 = Qn+uQn (a) When r = u = 1, s = 0.75, v = 0.50, K₁ = 1200 and K2 = 1000 the two species reach a non-zero equilibrium, meaning that the two populations can continue to coexist. Make a graph that illustrates the populations starting with initial populations of Po= 500 and Qo = 200 and approaching this equilibrium. (b) Find values of r, s, u and v such that species P dies out, and species Q approaches its carrying capacity K2. Write the values of r, s, u and v that you found, along with the initial population values that you used, on your paper. Include a graph that illustrates this behavior.

Advanced Engineering Mathematics
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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15. Use a spreadsheet for this problem, and attach your results in your PDF submission. There is a template of a Google Sheets you may use in the Course Calendar, but the formulas do NOT reflect the ones below and you will have to adjust them. Consider the following model of competition between two species, P and Q: Pn+1 = Pn+rPn- Qn+1 K₁-Pn-sQn K₁ K2-Qn-vPn K₂ = Qn+uQn (a) When r = u = 1, s = 0.75, v = 0.50, K₁ = 1200 and K2 = 1000 the two species reach a non-zero equilibrium, meaning that the two populations can continue to coexist. Make a graph that illustrates the populations starting with initial populations of Po = 500 and Qo = 200 and approaching this equilibrium. (b) Find values of r, s, u and v such that species P dies out, and species Q approaches its carrying capacity K2. Write the values of r, s, u and v that you found, along with the initial population values that you used, on your paper. Include a graph that illustrates this behavior.
Transcribed Image Text:15. Use a spreadsheet for this problem, and attach your results in your PDF submission. There is a template of a Google Sheets you may use in the Course Calendar, but the formulas do NOT reflect the ones below and you will have to adjust them. Consider the following model of competition between two species, P and Q: Pn+1 = Pn+rPn- Qn+1 K₁-Pn-sQn K₁ K2-Qn-vPn K₂ = Qn+uQn (a) When r = u = 1, s = 0.75, v = 0.50, K₁ = 1200 and K2 = 1000 the two species reach a non-zero equilibrium, meaning that the two populations can continue to coexist. Make a graph that illustrates the populations starting with initial populations of Po = 500 and Qo = 200 and approaching this equilibrium. (b) Find values of r, s, u and v such that species P dies out, and species Q approaches its carrying capacity K2. Write the values of r, s, u and v that you found, along with the initial population values that you used, on your paper. Include a graph that illustrates this behavior.
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