The second part of Hilbert's 16th problem not only concerns "The number of limit cycles of a polynomial vector field", but also the position and configuration of of those limit cycles with respect to each other. However the primary and the usual interpretation of the concept "Relative Position" is that "Whether two given limit cycles are nested closed curves or not" but the following post is a motivation to consider other types of questions about configuration of limit cycles, for example "Can two nested limit cycles have opposite orientation?"

A cubic system with two nested limit cycles with opposite orientations

In this regard we focus on cubic polynomial system and ask the following question:

What is an example of **Cubic** polynomial vector field $$\begin{cases} x'=P(x,y)\\ y'=Q(x,y) \end{cases}$$ such that two nested 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 $C_2$?

There is a very interesting example of degree $5$ here but we search for degree $3$