Predicting period-doubling bifurcations in nonlinear time-delayed feedback systems

A graphical approach is developed in this paper for detecting the period-doubling bifurcation emerging near the Hopf bifurcation point of a time-delayed feedback system. The new algorithm employs higher-order harmonic balance approximations (HBAs) for estimating the predicted periodic solutions of the system. Prediction of the period-doubling bifurcation is accomplished using a type of distortion index based on some information about the higher-order harmonics. The time-delayed Chua´s circuit is used as an example for illustration