Chaos, coexisting attractors, and fractal basin boundaries in DC drives with full-bridge converter

The existence of period-doubling bifurcation cascades and chaos in DC drives with full-bridge converter is well known. This paper reports for the first time the occurrence of coexisting attractors with a fractal basin of attraction in this relatively simple deterministic system. At some parameter values the trajectories converge on either a period-1 or a period-3 attracting set depending on the initial state of the system. The attempt to separate the basins of attractions of each attracting set revealed the existence of a riddled basin of attraction. This phenomenon has practical consequences in that it might render future prediction of the system´s steady state behavior almost impossible. Using Filippov´s method, we show analytically that the co-existing period-3 attractor is born due to a saddle node bifurcation that occurs at some critical parameter value, and thus it co-exists with the stable period-1 attractor.