Analysis of bifurcation and chaos in a class of piecewise smooth systems based on symbolic sequence

Based on the sequence of circuit topologies, a symbolic sequence method is proposed for analyzing the bifurcations and chaos in a class of piecewise smooth systems like DC/DC converters. The largest subsequence (LS) is used to distinguish the type of bifurcation and detect border collision bifurcation e. g., when a period-doubling bifurcation occurs, the LS is unchanged; when border collision bifurcation occurs, the LS is changed; and when chaos occurs, the LS does not exist. It is shown that the duty ratio is an essential variable for describing the nonlinear dynamics of a class of piecewise smooth systems like DC/DC converters, and saturating nonlinearity is the root cause of border collision bifurcation.