What is  an example  of  polynomial vector  field  $$\begin{cases} x'=P(x,y)\\ y'=Q(x,y) \end{cases}$$  such that two closed orbits $C_1,C_2$ of the system surrounds  an annular  region $R$ such that $R$ does  not contain any  singular point and the flow orientation of $C_1$  is opposite  to the  flow-orientation of  $C_2$.

The  motivation for this  question is the  following [counterexample  of  a  nongeodesible flow on the  torus](https://mathoverflow.net/questions/273635/finding-a-1-form-adapted-to-a-smooth-flow/273689#273689) and [the  following post](https://mathoverflow.net/questions/160945/limit-cycles-as-closed-geodesicsin-negatively-or-positively-curved-space?noredirect=1&lq=1).

Note that this  situation can not be  occurred  when the  degree of  $P,Q$ is at most $2$. See theorem $4$ [of the  following paper.](https://www.sciencedirect.com/science/article/pii/0022039666900702).So we  search  for  a  cubic (or  higher degree ) system.