stability in the periodic orbit and in the singular point <mover> x &#x02D9;<!-- ˙ --

taghdh9

taghdh9

Answered question

2022-06-24

stability in the periodic orbit and in the singular point
x ˙ = y + λ x ( 36 9 x 2 y 2 ) y ˙ = 9 x + λ y ( 36 9 x 2 y 2 ) z ˙ = 6 z λ 2 x 2 y 2 z 3
I want to analyze the stability in the periodic orbit and in the singular point, so for the singular point I take the derived matrix of the linear part, and I got the eigenvalues, wich are λ 1 = 6, λ 2 = 3 i , λ = 3 i . I wanted to use Andronov-Vitt but I have two eigenvalues with no real part so I can´t, does anybody can help me with this?

Answer & Explanation

scoseBexgofvc

scoseBexgofvc

Beginner2022-06-25Added 20 answers

It appears that you have an issue with the Jacobian and hence the eigenvalues.
There is one critical point at ( x , y , z ) = ( 0 , 0 , 0 )
Evaluating J ( x , y , z ) at this critical points yields the eigenvalues:
λ 1 = 6 , λ 2 = 36 λ 3 i , λ 3 = 36 λ + 3 i

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?