## Periodic Solutions in Non-Linear systems

Hi Guys,

I have a question about showing that the system has a periodic solution.
$
\dot{x}=x-y-x^3=f(x,y)
$

$
\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?