CDS 140a Winter 2014 Homework 9

R. Murray	Issued: 25 Feb 2014 (Tue)
ACM 101b/AM 125b/CDS 140a, Winter 2014 (PDF)	Due: 5 Mar 2014 (Wed) @ noon

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1. Perko, Section 4.4, Problem 1a
Show that for $a + b \neq 0$ the system <amsmath>

 \aligned
   \dot x &= \mu x - y + a (x^2 + y^2) x - b (x^2 + y^2) y + O(|x|^4) \\
   \dot y &= x + \mu y + a (x^2 + y^2) x + b (x^2 + y^2) y + O(|x|^4)
 \endaligned

</amsmath>

has a Hopf bifurcaton at the origin at the bifurcation value $\mu = 0$. Determine whether it is supercritical or subcritical.