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2. Given the system of differential equations a' = 0.2x -0.005xy, y'= -0.5y +0.01.xy, which models the rates of changes of two interacting species populations, describe the type of x- and y-populations involved (exponential or logistic) and the nature of their interaction (competition, cooperation, or predation). Then find and characterize the system's critical points (type and stability). Determine what nonzero x- and y-populations can coexist. Then construct a phase plane portrait that enables you to describe the long term behavior of the two populations. Use https://www.geogebra.org/m/utcMvuUy to confirm your results.

2. Given the system of differential equations a' = 0.2x -0.005xy, y'= -0.5y +0.01.xy, which models the rates of changes of two interacting species populations, describe the type of x- and y-populations involved (exponential or logistic) and the nature of their interaction (competition, cooperation, or predation). Then find and characterize the system's critical points (type and stability). Determine what nonzero x- and y-populations can coexist. Then construct a phase plane portrait that enables you to describe the long term behavior of the two populations. Use https://www.geogebra.org/m/utcMvuUy to confirm your results.

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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2. Given the system of differential equations x' = 0.2x -0.005xy, y'= -0.5y +0.01.xy, which models the rates of changes of two interacting species populations, describe the type of x- and y-populations involved (exponential or logistic) and the nature of their interaction (competition, cooperation, or predation). Then find and characterize the system's critical points (type and stability). Determine what nonzero x- and y-populations can coexist. Then construct a phase plane portrait that enables you to describe the long term behavior of the two populations. Use https://www.geogebra.org/m/utcMvuUy to confirm your results. Y X
Transcribed Image Text:2. Given the system of differential equations x' = 0.2x -0.005xy, y'= -0.5y +0.01.xy, which models the rates of changes of two interacting species populations, describe the type of x- and y-populations involved (exponential or logistic) and the nature of their interaction (competition, cooperation, or predation). Then find and characterize the system's critical points (type and stability). Determine what nonzero x- and y-populations can coexist. Then construct a phase plane portrait that enables you to describe the long term behavior of the two populations. Use https://www.geogebra.org/m/utcMvuUy to confirm your results. Y X
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