Consider the dynamical system: Select the only correct statement. dt dx = x - y - x(x² + y²) = x + y − y(x² + y²) = 1 dy dt This system has no limit cycle, but is not a gradient system. This is a gradient system. A limit cycle exist on the circle of radius 1 centered at the origin. A trapping region for the Poincare-Bendixon theorem is the annulus ≤r≤ 1.
Consider the dynamical system: Select the only correct statement. dt dx = x - y - x(x² + y²) = x + y − y(x² + y²) = 1 dy dt This system has no limit cycle, but is not a gradient system. This is a gradient system. A limit cycle exist on the circle of radius 1 centered at the origin. A trapping region for the Poincare-Bendixon theorem is the annulus ≤r≤ 1.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 31E
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Transcribed Image Text:Consider the dynamical system:
Select the only correct statement.
dx
dt
= x - y = x (x² + y²)
-
dy = x+y= y(x² + y²)
dt
This system has no limit cycle, but is not a gradient system.
This is a gradient system.
A limit cycle exist on the circle of radius 1 centered at the origin.
A trapping region for the Poincare-Bendixon theorem is the annulus
≤r≤1.
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