Figure 2
From: Exploring the geometry of the bifurcation sets in parameter space
One-plus-one geometric bifurcations exhibited in three-parameter spaces. Top: The bifurcation surface M reaches a maximum value at \(\varepsilon =0\). Exploring the surface with horizontal planes, an equivalence class (cyan) disappears because the limiting bifurcation curve (red circle) collapses to a point when \(\varepsilon =0\) (top right panel). Bottom: The bifurcation surface has a saddle point. Passing through \(\varepsilon =0\), the bifurcation curves (red branches of a hyperbola) change their position with respect to the asymptotes. As a consequence, the equivalence class around the central point switches (bottom right panel).
