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

Abstract

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.