Boundary intersection crossing bifurcation in the presence of sliding
The paper deals with a class of discontinuity induced bifurcations that result from interactions between periodic orbits and the intersection of two or more discontinuity boundaries (between periodic orbits and corners of discontinuity boundaries). The wide variety of qualitatively different configurations makes the analysis of such bifurcations very difficult. The author starts with some observations on uniqueness of solutions in the presence of boundary intersections. Then the concepts of zero-time discontinuity mapping and Poincaré discontinuity mapping are explained, and the discontinuity mapping is derived in a quite general setting for the case of two intersecting boundaries in the presence of sliding. The results are applied to the analysis of a model of a buck converter. The ideas proposed in the paper can be implemented in bifurcation analysis software for the characterization of discontinuity induced bifurcations and the detection of bifurcations of higher codimensions.
boundary intersection crossing bifurcation
scientific article; zbMATH DE number 5506294
scientific article