MAT244-2014F > MAT244 Math--Lectures

How can I decide what type of the local phase portrait is

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Li:
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:
Generally from linearized system you cannot tell center from a spiral point. So your correct answer should be "it is either center or a spiral point" but you also should indicate  if it is clock-wise or counter-clock-wise oriented.

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