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2.3 Consider the nonlinear system =y+x(x² + y2-1) sin. y=-x + y (x² + y2 - 1) sin 1 ² + y² - 1 1 x²+y²-1 Without solving the above equations explicitly, show that the system has infinite number of limit cycles. Determine the stability of these limit cycles. (Hint: Use polar coordinates.)

2.3 Consider the nonlinear system =y+x(x² + y2-1) sin. y=-x + y (x² + y2 - 1) sin 1 ² + y² - 1 1 x²+y²-1 Without solving the above equations explicitly, show that the system has infinite number of limit cycles. Determine the stability of these limit cycles. (Hint: Use polar coordinates.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 31E
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2.3 Consider the nonlinear system *=y+x(x² + y2 - 1) sin 1 x²+) y = -x + y (x² + y² - 1) sin 1 x² + y²-1 Without solving the above equations explicitly, show that the system has infinite number of limit cycles. Determine the stability of these limit cycles. (Hint: Use polar coordinates.)
Transcribed Image Text:2.3 Consider the nonlinear system *=y+x(x² + y2 - 1) sin 1 x²+) y = -x + y (x² + y² - 1) sin 1 x² + y²-1 Without solving the above equations explicitly, show that the system has infinite number of limit cycles. Determine the stability of these limit cycles. (Hint: Use polar coordinates.)
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