Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Again I have this:

$\dot{x}=-y+\lambda x(36-9x^2-y^2)\\\dot{y}=9x+\lambda y(36-9x^2-y^2)\\\dot{z}=-6z-\lambda^2x^2y^2z^3$

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 $\lambda_1=-6$ , $\lambda_2=3i$ , $\lambda=-3i$ . 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? Thanks!

share|improve this question

1 Answer 1

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:

$$\lambda_1 = -6, \lambda_2 = 36 \lambda -3 i, \lambda_3 = 36 \lambda + 3 i$$

share|improve this answer
    
am ok, but then i have to considered all the equation and not only the linear part? because that was that i want to do –  k73586 Dec 9 '13 at 7:17
    
I am sorry, but I do not understand your comment. Are you saying you understand what I did, but now want to consider the nonlinear part as well? –  Amzoti Dec 9 '13 at 13:45
    
Frustrating...change the question completely! +1 for the nice work. –  amWhy Dec 10 '13 at 0:03
    
... and a very difficult question to boot! :-) –  Amzoti Dec 10 '13 at 1:56

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.