Non-observable chaos in piecewise smooth systems

Abstract

In the present paper, we discuss bifurcations of chaotic attractors in piecewise smooth one-dimensional maps with a high number of switching manifolds. As an example, we consider models of DC/AC power electronic converters (inverters). We demonstrate that chaotic attractors in the considered class of models may contain parts of a very low density, which are unlikely to be observed, neither in physical experiments nor in numerical simulations. We explain how the usual bifurcations of chaotic attractors (merging, expansion and final bifurcations) in piecewise smooth maps with a high number of switching manifolds occur in a specific way, involving low-density parts of attractors, and how this leads to an unusual shape of the bifurcation diagrams.