Representative phase portraits of (1.10) showing the invariant objects in the topologically different regions A–F as described in Fig. 1(⁠|$a$|⁠). Sources, saddles and sinks are represented by , and , respectively, with equilibria and periodic orbits coloured and labelled as described in Fig. 1. Also shown are the stable manifolds (light-blue curve) and the unstable manifolds (orange curve), and the strong unstable manifold (orange) in region |$\boldsymbol {F}$|⁠. The basins of attraction () and repulsion ( and ) of the left invariant object in a symmetric pair of equilibria or periodic orbits are shaded green and pink, respectively.