Suppose a competing species system with variables = representing rabbits and s representing sheep, has critical points (r, s), with r r° = = (0,0), x¹ = (0,3), x² = (3,0), and x³ = (1,1). (0,0), Also assume that: . is a source node; ¹ and ² are saddle nodes; 3 ³ is a sink node where one eigenvector points in the direction of , while another eigenvector 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 = representing rabbits and s representing sheep, has critical points (r, s), with r r° = = (0,0), x¹ = (0,3), x² = (3,0), and x³ = (1,1). (0,0), Also assume that: . is a source node; ¹ and ² are saddle nodes; 3 ³ is a sink node where one eigenvector points in the direction of , while another eigenvector 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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![Suppose a competing species system with variables =
representing rabbits and s representing sheep, has critical points
(r, s), with r
r° =
= (0,0), x¹ = (0,3), x² = (3,0), and x³ = (1,1).
(0,0),
Also assume that:
.
is a source node;
¹ and ² are saddle nodes;
3
³ is a sink node where one eigenvector points in the direction of , while
another eigenvector 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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0695e04c-6177-4dae-ae8e-62e62853c8ae%2Fae4d5f9e-a21b-422b-8dba-aea2f4db636e%2Fiuejhnq_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose a competing species system with variables =
representing rabbits and s representing sheep, has critical points
(r, s), with r
r° =
= (0,0), x¹ = (0,3), x² = (3,0), and x³ = (1,1).
(0,0),
Also assume that:
.
is a source node;
¹ and ² are saddle nodes;
3
³ is a sink node where one eigenvector points in the direction of , while
another eigenvector 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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