Codimension-3 Bifurcation for Continuous Saddle Bimodal Linear Dynamical Systems

We continue the study of the structural stability and the bifurcations of planar continuous bimodal linear dynamical systems (that is, systems consisting of two linear dynamics acting on each side of a straight line, assuming continuity along the separating line). Here, we complete the study when one of the subsystems is a saddle, leading to a 3D bifurcation diagram where a large catalogue of bifurcations appears: four surfaces of codimension-1 bifurcations; two sequences of surfaces of additional codimension-1 bifurcations; two lines of codimension-2 bifurcations; and one codimension-3 bifurcation.