Complex instabilities near codimension-2 bifurcation and torus breakdown in a Cuk converter with an inductive impedance load

Power switching converters exhibit a wide range of nonlinear behavior, such as bifurcation and chaos. Complex instabilities near the codimension-2 bifurcation point are shown in some nonlinear higher order systems. In this study, codimension-2 bifurcation and complex instabilities in a single inner current loop controlled Cuk converter with an inductive impedance load are analyzed by studying the Floquet multipliers and switching modes of the system. The period1 orbit loses its stability by period-doubling and subcritical Neimark-Sacker bifurcations. The period2 orbit enters a two-loop torus orbit via border collision and Neimark-Sacker bifurcations. The dynamic behavior of the system near the codimension-2 bifurcation points is clearly studied. The mechanism of the coexisting phenomenon from the subcritical Neimark-Sacker bifurcation is explained. Finally, chaos from torus breakdown is detected in this higher order switching converter with an inductive impedance load and its phase shift characteristics to different initial conditions are investigated.