Detecting period-doubling bifurcation: an approximate monodromy matrix approach

A quasi-analytical approach is developed for detecting period-doubling bifu rcation emerging near a Hopf bifurcation point. The new algorithm employs h igher-order Harmonic Balance Approximations (HBAs) to compute the monodromy matrix, useful for the study of limit cycle bifurcations. Prediction of th e period-doubling bifurcation is accomplished very accurately by using this algorithm, along with a detailed approximation error analysis, without usi ng numerical integration of the dynamical system. An example is given to il lustrate the results. (C) 2001 Elsevier Science Ltd. All rights reserved.