Multistability and hidden attractors in a multilevel DC/DC converter

• Demonstration of a torus fold instability that produces hidden attractors.
• Investigation of hidden attractors in piecewise-smooth systems.
• Study of mutually embedded stable tori in a DC/DC converter.

An attracting periodic, quasiperiodic or chaotic set of a smooth, autonomous system may be referred to as a “hidden attractor” if its basin of attraction does not overlap with the neighborhood of an unstable equilibrium point. Historically, this condition has implied that the basin of attraction for the hidden set in most cases has been so complicated that special analytic and/or numerical techniques have been required to locate the set. By simulating the model of a multilevel DC/DC converter that operates in the regime of high feedback gain, the paper illustrates how pulse-width modulated control can produce complicated structures of attracting and repelling states organized around the basic switching cycle. This leads us to suggest the existence of hidden attractors in such systems as well. In this case, the condition will be that the basin of attraction does not overlap with the fixed point that represents the basic switching cycle.