Quasiperiodicity and torus birth bifurcations in nonsmooth systems

Considering a pulse-width modulated DC/DC converter as an example, this paper describes a new type of border-collision bifurcation that can occur in multidimensional piecewise-smooth dynamical systems displaying a quasiperiodic route to chaos. We demonstrate how a two-dimensional torus can arise from a periodic orbit through a bifurcation in which two complex-conjugate Poincare characteristic multipliers jump abruptly from the inside to the outside of the unit circle. The torus may be ergodic or resonant. However, in both cases the diameter of the torus develops approximately linearly with the distance to the bifurcation point as opposed to the characteristic parabolic form of the well-known Neimark-Sacker bifurcation.