Figure 8.

The choice landscape: the dual cusp. (a) Bifurcation set. The solid lines show the bifurcation set. The dashed arrow shows a path in parameter space. In the region R₂ (inside the cusp, above), there are three attractors separated by two saddles. When the parameters move out of R₂ to R₁ (outside the cusp, below) by crossing ${\mathcal{B}}_1$ (respectively, ${\mathcal{B}}_2$) the central attractor (blue) and the right (respectively, left) saddle undergo a fold bifurcation which destroys the attractor. (b) The path (γ₁) indicated gives a 1D representation of the choice family and the available transitions from the central attractor. The duality between the hysteresis diagram and the middle part of this diagram is apparent. (c) The path (γ₂) indicated shows a pitchfork bifurcation where the central saddle becomes two saddles and a new attractor. The duality between this diagram and figure 7c is apparent.