
Periodic Orbits
Ok i'm kinda stuck on this question. I need to show that this system has periodic orbits.
x'=2x+yx^2x^3
y'=3xy+(1/3)X^3
The question tells me to use the PoincareBendixson 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