Hi Guys,

I have a question about showing that the system has a periodic solution.

$\displaystyle

\dot{x}=x-y-x^3=f(x,y)

$

$\displaystyle

\dot{y}=x+y-y^3=g(x,y)

$

This was under the poincarre-bendixson theorem section.

As an alternative to using that theorem, can I just linearize it and show that the origin is an unstable center thus showing that it has a periodic solution?