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For each of the systems below, sketch the phase portrait. Make sure to include nullclines, equilibria and their stability. (a) Two competing species: x' = 3x – x2 – xy, y' = 5y – 2y² – xy, x, y > 0

For each of the systems below, sketch the phase portrait. Make sure to include nullclines, equilibria and their stability. (a) Two competing species: x' = 3x – x2 – xy, y' = 5y – 2y² – xy, x, y > 0

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. For each of the systems below, sketch the phase portrait. Make sure to include nullclines, equilibria and their stability. (a) Two competing species: a' = 3x – x? – xy, y' = 5y – 2y² – xy, x, y > 0 (b) Predator-prey system: x' = 3x – x2 – xy, y' = -5y + 2y² + xy, X, y > 0 (c) Two competing species: a' = 3x – a? – y, y = 5y – y? – 2.xy, x, y > 0
Transcribed Image Text:4. For each of the systems below, sketch the phase portrait. Make sure to include nullclines, equilibria and their stability. (a) Two competing species: a' = 3x – x? – xy, y' = 5y – 2y² – xy, x, y > 0 (b) Predator-prey system: x' = 3x – x2 – xy, y' = -5y + 2y² + xy, X, y > 0 (c) Two competing species: a' = 3x – a? – y, y = 5y – y? – 2.xy, x, y > 0
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