Suppose a competing species system with variables = (r, s), with representing rabbits and s representing sheep, has critical points = (0,0), x¹ = (0,3), x² (0,3), x² = (3,0), =(3,0), and x³ = (1,1) Also assume that: is a source node; • ¹ and ² are sink nodes; • ³ is a saddle node where the eigenvector with negative eigenvalue points in the direction of x, while the eigenvector with positive eigenvalue points approximately in the directions of x¹, x² What does this system predicts about the populations of the two species given any physically realistic initial data?
Suppose a competing species system with variables = (r, s), with representing rabbits and s representing sheep, has critical points = (0,0), x¹ = (0,3), x² (0,3), x² = (3,0), =(3,0), and x³ = (1,1) Also assume that: is a source node; • ¹ and ² are sink nodes; • ³ is a saddle node where the eigenvector with negative eigenvalue points in the direction of x, while the eigenvector with positive eigenvalue points approximately in the directions of x¹, x² What does this system predicts about the populations of the two species given any physically realistic initial data?
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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Transcribed Image Text:Suppose a competing species system with variables = (r, s), with
representing rabbits and s representing sheep, has critical points
xº = (0,0), x¹ = (0,3), x² = (3,0), and x³ = (1,1)
Also assume that:
is a source node;
• ¹ and ² are sink nodes;
x²
³ is a saddle node where the eigenvector with negative eigenvalue points in
.
.
the direction of , while the eigenvector with positive eigenvalue points
approximately in the directions of x¹, x².
What does this system predicts about the populations of the two species given any
physically realistic initial data?
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