Ok i'm kinda stuck on this question. I need to show that this system has periodic orbits.

x'=2x+y-x^2-x^3

y'=-3x-y+(1/3)X^3

The question tells me to use the Poincare-Bendixson Theorem.

-But this is what i got so far i need 2 boundary functions

-Inner boundary of my annulus i'm thinking i need to use an ellipse

-Outer boundary of my annulus i'm thinking i need to use a rectangle

Now this is where i'm stuck, was wondering if someone could give me some pointers. Mainly how to start the question. Anything would be great. Thanks