Hopf bifurcation and chaos in a hysteretic current-controlled Cuk regulator

A free-running Cuk power converter is studied in this paper. An autonomous state equation and its dimensionless form are derived. Analysis of this equation shows that the system loses stability via a supercritical Hopf bifurcation. The boundary of stability is derived and trajectories of motion studied. In the unstable region, the largest Lyapunov exponent is positive, verifying the chaotic operation. Computer simulations of the actual system and experimental results verify the analytical results regarding stability and chaos.