Quasi-periodicity and border-collision bifurcations in a DC-DC converter with pulsewidth modulation

The paper considers the dynamics of a dc-dc converter with pulsewidth modulation. The typical scenario for the transition to chaos in such systems proceeds via quasi-periodicity, resonance cycles, and torus destruction. Detailed bifurcation analysis shows that the resonance solutions arise via border-collision bifurcations (BCB) on a two-dimensional torus. The arrangement of the resonance domains within the parameter plane is related to the Farey series, and their internal structure is described. It is shown that transitions to chaos mainly occur through finite sequences of BCB. Some other possible causes of complex dynamics are considered, including a subcritical Neimark-Sacker (Andronov-Hopf) bifurcation and the associated hysteretic phenomena.