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