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arXiv · 2210.14445

A synopsis of the non-invertible, two-dimensional, border-collision normal form with applications to power converters

Hammed Olawale Fatoyinbo·David J. W. Simpson
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Abstract

The border-collision normal form is a canonical form for two-dimensional, continuous maps comprised of two affine pieces. In this paper we provide a guide to the dynamics of this family of maps in the non-invertible case where the two pieces fold onto the same half-plane. We identify parameter regimes for the occurrence of key bifurcation structures, such as period-incrementing, period-adding, and robust chaos. We then apply the results to a classic model of a boost converter for adjusting the voltage of direct current. It is known that for one combination of circuit parameters the model exhibits a border-collision bifurcation that mimics supercritical period-doubling and is non-invertible due to the switching mechanism of the converter. We find that over a wide range of parameter values, even though the dynamics created in border-collision bifurcations is in general extremely diverse, the bifurcation in the boost converter can only mimic period-doubling, although it can be subcritical.

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Hammed Olawale Fatoyinbo, David J. W. Simpson. 2022-10-26. A synopsis of the non-invertible, two-dimensional, border-collision normal form with applications to power converters. https://doi.org/10.1142/s0218127423300197

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