Border collision bifurcations and chaos in a class of piecewise smooth systems with two boundaries

A class of piecewise smooth maps with three zones is derived to describe the dynamics of a current-programmed Buck-Boost converter operating in a discontinuous mode. The numerical simulation is carried out and the bifurcation diagrams with the input voltage as a parameter are obtained. It is shown that, when a bifurcation occurs, some eigenvalues of the Jacobian matrix jumps over the unit circle in a discontinuous way, and there are always some orbit points lying on the boundaries which separate different regions in the phase plane. It is concluded that border collision bifurcations could occur when the input voltage varies, for example, a bifurcation from a periodic orbit to another periodic orbit or chaotic orbit.