Take the Van Der Pol equation x" — 6(1-x²)x' + x = 0. Write down the corresponding first order system using the extra variable y: x' = y' = Compute the Jacobian matrix for all x and y: There is a critical point at the origin. The behavior is For behavior write one of "saddle", "source", "sink", "spiral sink", "spiral source", "center".
Take the Van Der Pol equation x" — 6(1-x²)x' + x = 0. Write down the corresponding first order system using the extra variable y: x' = y' = Compute the Jacobian matrix for all x and y: There is a critical point at the origin. The behavior is For behavior write one of "saddle", "source", "sink", "spiral sink", "spiral source", "center".
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Systems Of Linear Equations
Section1.1: Introduction To Systems Of Linear Equations
Problem 72E: Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by...
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![Take the Van Der Pol equation x" — 6(1-x²)x² + x = 0.
Write down the corresponding first order system using the extra variable y:
x' =
y' =
Compute the Jacobian matrix for all x and y:
There is a critical point at the origin. The behavior is
For behavior write one of "saddle","source", "sink", "spiral sink", "spiral source", "center".](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ea01508-f9b6-4a19-b038-56e12c298daf%2F416d82e1-90f0-4791-8123-8a09a0ff0ff3%2Fmr1llkm_processed.png&w=3840&q=75)
Transcribed Image Text:Take the Van Der Pol equation x" — 6(1-x²)x² + x = 0.
Write down the corresponding first order system using the extra variable y:
x' =
y' =
Compute the Jacobian matrix for all x and y:
There is a critical point at the origin. The behavior is
For behavior write one of "saddle","source", "sink", "spiral sink", "spiral source", "center".
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