Figure 12.

Families with flip curves. (a,b) Bifurcation sets. The bifurcation sets for two landscape families: the solid lines indicate fold curves and the dashed lines are flip curves. The colour of the fold line corresponds to the attractor involved in the fold bifurcation. Examples of landscapes in the family are sketched. Both families contain the flip landscape in the areas marked in green. (a) One flip with a cusp. The two attractors connected to the sink saddle can undergo a cusp bifurcation. (b) With no cusps. This family contain three instances of the flip landscape. The region enclosed by the blue deltoid corresponds to landscapes with an extra pair of critical points: a saddle and either a repellor or an attractor (as shown in the blue box). Generically, the flip curves enter the deltoid avoiding the cusps and terminate in one of the three smooth edges of the deltoid. This family is part of the compactified elliptic umbillic catastrophe.