A quasi-analytical approach to period-doubling bifurcation computation and prediction

A quasi-analytical approach is developed in this paper for detecting the period-doubling bifurcation emerging near a Hopf bifurcation point. The new algorithm employs higher-order harmonic balance approximations (HBAs) to compute the monodromy matrix, which is useful for the study of bifurcations. Prediction of the period-doubling bifurcation is accomplished very accurately by using this computational procedure. An example is given to illustrate the main results, with an application to the delay control of the period-doubling bifurcation.