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Problem : Consider the following van der Pol oscillator: x+µ(x² − 1)x + x = 0 a) Show that the oscillator can be expressed as: x=y−µ -- (²3-²-x) y = -x b) Find the values of µ and x that make V = (x² + y²)/2 a Lyapunov function for the system. What is the stability of the origin for those values of μ and x?

Problem : Consider the following van der Pol oscillator: x+µ(x² − 1)x + x = 0 a) Show that the oscillator can be expressed as: x=y−µ -- (²3-²-x) y = -x b) Find the values of µ and x that make V = (x² + y²)/2 a Lyapunov function for the system. What is the stability of the origin for those values of μ and x?

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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Problem : Consider the following van der Pol oscillator: *+µ(x² - 1)x + x = 0 a) Show that the oscillator can be expressed as: x=y-μ * =y -- (²3-3-X) y = -x b) Find the values of u and x that make V = (x² + y²)/2 a Lyapunov function for the system. What is the stability of the origin for those values of μ and x?
Transcribed Image Text:Problem : Consider the following van der Pol oscillator: *+µ(x² - 1)x + x = 0 a) Show that the oscillator can be expressed as: x=y-μ * =y -- (²3-3-X) y = -x b) Find the values of u and x that make V = (x² + y²)/2 a Lyapunov function for the system. What is the stability of the origin for those values of μ and x?
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