Figure 2.

Two-dimensional landscapes. (a) System with three attractors and two saddles. The purple curves are the separatrices or stable manifolds of the saddles, the red curves are the unstable manifolds (if time is run backwards points on these converge to the saddle). Points on each unstable manifold converge to two attractors and the stable manifolds divide the phase space into three basins, one for each attractor. Level curves for the saddles are indicated in black. (b) Saddle point. The dynamics near a saddle point. The stable (purple) and unstable (red) manifolds are shown.