- #1
ugresearcher
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Homework Statement
Consider the system x''+ax'(x2+x'2-1)+x = 0, where a>0.
a)Find and classify all the fixed points.
b)Show that the system has a circular limit cycle, and find its amplitude and period.
c)Determine the stability of the limit cycle.
Homework Equations
y = x'
For fixed points: x'=0, y'=0.
The Attempt at a Solution
Using y=x', the system becomes:
x' = y
y' = -ax'(x2+x'2-1)-x
Using x' = 0 and y' = 0, 1 Fixed point exists at (0,0).
I'm not sure where to go from here. The problem is in Chapter 7, section 1 of "Nonlinear Dynamics and Chaos" by Strogatz.