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Find general formulas (in terms of R, a, f, q, and K) for the equilibrium point in the predator-prey model with logistic prey growth. In other words, find the values of V and C for which, once the populations reach those values, they will never change.

Find general formulas (in terms of R, a, f, q, and K) for the equilibrium point in the predator-prey model with logistic prey growth. In other words, find the values of V and C for which, once the populations reach those values, they will never change.

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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1. Build the predator-prey model with logistic prey growth in a spreadsheet, using parameter values R=0.25, a=0.01, q=0.1, f-0.008, initial populations of 1000 and 20, and carrying capacity 3000. Run the model for 100 time steps and create a time plot and a phase plane plot. 2. Find general formulas (in terms of R, a, f, q, and K) for the equilibrium point in the predator-prey model with logistic prey growth. In other words, find the values of V and C for which, once the populations reach those values, they will never change. 3. Type the formulas you found in (2) into your spreadsheet to compute the equilibrium point for the model parameters in (1), and discuss whether the model seems to be approaching the equilibrium point. 4. Experiment with different values of R, a, f, and q until you find a combination that causes extinction of one or both species. Write down these parameter values. What do you notice about the overall behavior of the model while doing this exploration?
Transcribed Image Text:1. Build the predator-prey model with logistic prey growth in a spreadsheet, using parameter values R=0.25, a=0.01, q=0.1, f-0.008, initial populations of 1000 and 20, and carrying capacity 3000. Run the model for 100 time steps and create a time plot and a phase plane plot. 2. Find general formulas (in terms of R, a, f, q, and K) for the equilibrium point in the predator-prey model with logistic prey growth. In other words, find the values of V and C for which, once the populations reach those values, they will never change. 3. Type the formulas you found in (2) into your spreadsheet to compute the equilibrium point for the model parameters in (1), and discuss whether the model seems to be approaching the equilibrium point. 4. Experiment with different values of R, a, f, and q until you find a combination that causes extinction of one or both species. Write down these parameter values. What do you notice about the overall behavior of the model while doing this exploration?
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