The $GL(2,{\mathbb R})$-orbits of polynomial differential systems of degree four

In this paper we characterize the $GL(2,{\mathbb R})-$orbits of the differential systems $\dot{x}_1=P(x_1,x_2)$, $\dot{x}_2=Q(x_1,x_2),$ where $P,Q$ are polynomials of degree four, with respects to their dimensions.