Border Collision and Heteroclinic Bifurcations in a 2D Piecewise Smooth Map

We consider a 2D piecewise smooth map originating from an application (acting as a discrete-time model of a DC/DC converter with pulse-width modulated multilevel control). We focus on several non-trivial transformations occurring in the phase space of this map under parameter variation. In particular, we describe the effect of a fold border collision bifurcation leading to the appearance of a pair of cycles, an attracting and a saddle one, a sequence of transformations of the basins of coexisting attractors, as well as heteroclinic bifurcations which result first in the destruction of an attracting closed resonant curve and then in the creation of another one such curve.