The following model represents the competition of two species with populations measured by x and y: x˙ = x(3 − 2x − 2y) y˙ = y(2 − x − y). Analyze these equations: find fixed points and their stability, sketch nullclines, sketch a rough phase portrait, and indicate the basins of attraction for any stable fixed points.
The following model represents the competition of two species with populations measured by x and y: x˙ = x(3 − 2x − 2y) y˙ = y(2 − x − y). Analyze these equations: find fixed points and their stability, sketch nullclines, sketch a rough phase portrait, and indicate the basins of attraction for any stable fixed points.
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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The following model represents the competition of two species with populations measured by x
and y:
x˙ = x(3 − 2x − 2y) y˙ = y(2 − x − y).
Analyze these equations: find fixed points and their stability, sketch nullclines, sketch a rough
phase portrait, and indicate the basins of attraction for any stable fixed points.
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Could you explain the basin of attraction in this phase portrait?
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