Non-visible transformations of chaotic attractors due to their ultra-low density in AC–DC power factor correction converters

Abstract

Recently, it has been shown that DC–AC and AC–DC power converters whose dynamics is governed by two vastly different frequencies lead to a special class of piecewise smooth models characterized by a practically unpredictable number of switching manifolds between partitions in the state space associated with different dynamics. In the previous publications, we have shown that transformations of chaotic attractors in such models can be caused by their interactions with unstable cycles occurring in the regions of the attractors associated with an ultra-low invariant density, which is beyond a practical observability in physical or numerical experiments. The appearance of such low-density regions has been explained by the so-called spiking phenomenon. In the present paper, we make the next step and ask the natural question what are the reasons behind the appearance of spikes. Applying a novel technique (cobweb diagrams for non-autonomous maps), we explain a connection between spiking and the presence of two vastly different frequencies.