March 25th, 2010, 02:34 AM  #1  
Newbie Joined: Mar 2010 Posts: 2 Thanks: 0  Linearizing ODEs
Hi all, I hope this finds everyone well. I'm having a bit of an issue with what seems to be a rather simple mathematical step. Yet, as hard as I try I'm still not coming out with the correct answer. Ok... as taken from the book Nonlinear Systems by P. G. Drazin, page 19, on Hopf Bifurcation: I have two ODEs: , and . First the author investigates their equilibirum points i.e., to find that x = y = 0. This is simple enough to understand. Next the author says: Quote:
So I've tried linearizing the two original ODEs yet I don't seem to get what the author does. If anyone can, could you please illustrate the steps. It's probably something so simple, yet it's driving me nuts. Thanks  
March 25th, 2010, 01:38 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,788 Thanks: 708  Re: Linearizing ODEs
All the author is saying is, that for small x and y, x^2 and y^2 can be neglected, as long as a ? 0.

March 25th, 2010, 04:19 PM  #3 
Newbie Joined: Mar 2010 Posts: 2 Thanks: 0  Re: Linearizing ODEs
Fantastic, thanks After having made the post, I took some time out then came back and it suddenly clicked! Thanks for confirming 

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