So the problem that I'm trying to solve is that this system has no closed orbit using the Bendixons' criteria.
$X' = Y + (X*(Y^2))$
$Y' = - Y + (Y*(X^2))$ .
My problem is at the origin $divF$ (system is F) becomes zero
and further the $\mathbb{R^2} $\ $(0,0)$ is not simply connected. So can we use Bendixons' criteria ?