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.
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