Time reversal of an autonomous differential equation ($\dot{z}=F(z)⟼\dot{z}=-F(z)$)

If $z(t)$ solves an autonomous differential equation, $w(t)=z(-t)$ solves the equation with negated vector field. The trajectories and equilibrium points stay in place but their orientations reverse; stable and unstable directions interchange. A saddle equilibrium remains a saddle, and a clockwise centre equilibrium becomes counterclockwise.