### Author Topic: How can I decide what type of the local phase portrait is  (Read 2261 times)

#### Li

• Newbie
• Posts: 2
• Karma: 0
##### How can I decide what type of the local phase portrait is
« on: December 05, 2014, 05:22:42 PM »
firstly, if the linear system I solved is center, how can I decide the locally linear system is center or spiral?
secondly, if the linear system I solved is two equal real eigenvalue, how can I decide wether it is node or spiral points?
I did the problem on the text book, in the answer it just said it is center or spiral, undetermined, do we need to write the exact type in final?

#### Victor Ivrii

As I explained if right-hand expressions are smooth and $r_1=r_2\ne 0$ then it will be either a proper node or improper nodeâ€”of the same type as for a linearized system. But it will not be considered as an error to answer "either node or spiral point" with indication if it is stable or unstable