CDS 140a Winter 2014 Homework 9
From Murray Wiki
Jump to navigationJump to search
R. Murray | Issued: 25 Feb 2014 (Tue) |
ACM 101b/AM 125b/CDS 140a, Winter 2014 | Due: 5 Mar 2014 (Wed) @ noon |
__MATHJAX__
Note: In the upper left hand corner of the second page of your homework set, please put the number of hours that you spent on this homework set (including reading).
- Perko, Section 4.4, Problem 1a Show that for $a + b \neq 0$ the system
\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.