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An extension of the logistic growth equation describing lynx population levels on an island y(t) (measured in hundreds at t years after 2000) is given by: dy - ky (1-2) (²-1) dt Assume N = 10, A = 2, and k = 5. (a) Draw the phase line to determine the equilibria, their stability, and a trajectory plot. 1 (b) Use an online software to generate the direction field. Draw the following solutions on top of your direction field: y(0) = 0, y(0) = 1, y(0) = 3, y(0) = 12. What do you notice? (c) What are the units of parameters k, N, and A? What are the biological interpre- tations of these parameters?

An extension of the logistic growth equation describing lynx population levels on an island y(t) (measured in hundreds at t years after 2000) is given by: dy - ky (1-2) (²-1) dt Assume N = 10, A = 2, and k = 5. (a) Draw the phase line to determine the equilibria, their stability, and a trajectory plot. 1 (b) Use an online software to generate the direction field. Draw the following solutions on top of your direction field: y(0) = 0, y(0) = 1, y(0) = 3, y(0) = 12. What do you notice? (c) What are the units of parameters k, N, and A? What are the biological interpre- tations of these parameters?

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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4. An extension of the logistic growth equation describing lynx population levels on an island y(t) (measured in hundreds at t years after 2000) is given by: dy dt Assume N 10, A = 2, and k = = = · ky (1 · (1 - 2 / ) (1/12 - ¹) N 5. (a) Draw the phase line to determine the equilibria, their stability, and a trajectory plot. 1 (b) Use an online software to generate the direction field. Draw the following solutions on top of your direction field: y(0) = 0, y(0) = 1, y(0) = 3, y(0) = 12. What do you notice? (c) What are the units of parameters k, N, and A? What are the biological interpre- tations of these parameters?
Transcribed Image Text:4. An extension of the logistic growth equation describing lynx population levels on an island y(t) (measured in hundreds at t years after 2000) is given by: dy dt Assume N 10, A = 2, and k = = = · ky (1 · (1 - 2 / ) (1/12 - ¹) N 5. (a) Draw the phase line to determine the equilibria, their stability, and a trajectory plot. 1 (b) Use an online software to generate the direction field. Draw the following solutions on top of your direction field: y(0) = 0, y(0) = 1, y(0) = 3, y(0) = 12. What do you notice? (c) What are the units of parameters k, N, and A? What are the biological interpre- tations of these parameters?
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