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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.

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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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.
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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