Critical Points and Linearization

Problem:

Determine the location and type of all critical points by linearization.

y1' = -y1 + y2 - (y2)**2

y2' = -y1 - y2

From the above, I set both equal to zero and determined the critical points to be (0,0) and (-2, 2).

This is where I get a little bit lost as to what to do next. It seems to me that I need to drop non-linear terms and find the eigenvalues.

y1' = -y1 + y2

y2' = -y1 - y2

In matrix form:

| -1-lambda 1 |

| -1 -1-lambda |

I compute lambda to be (-1 +/- i)

This is where I get completely lost and could use some help. Thanks in advance.

Re: Critical Points and Linearization

Got it! Thanks! Took me a while to learn more about how and when to determine the Jacobian, but now it looks fairly obvious to me what the process steps are in this type of problem. Wish my text book was as clear! (Happy)