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

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