A Frequency Domain Method for Analyzing Period Doubling Bifurcations in Discrete-Time Systems

A frequency domain methodology for the approximation of period doubling bifurcations in discrete-time nonlinear systems is presented. The computation of a stability index, which characterizes the dynamical behavior of the emerging period-two orbit is also derived. The technique is applied to estimate the domain of attraction of the fixed point in an adaptive control system and to improve the dynamical behavior of a buck converter.