Zou, KeguanNagarajaiah, Satish2014-10-072014-10-072014Zou, Keguan and Nagarajaiah, Satish. "An analytical method for analyzing symmetry-breaking bifurcation and period-doubling bifurcation." <i>Communications in Nonlinear Science and Numerical Simulation,</i> (2014) Elsevier: http://dx.doi.org/10.1016/j.cnsns.2014.08.015.https://hdl.handle.net/1911/77438A new modification of homotopy analysis method (HAM) is proposed in this paper. The auxiliary differential operator is specifically chosen so that more than one secular term must be eliminated. The proposed method can capture asymmetric and period-2 solutions with satisfactory accuracy and hence can be used to predict symmetry-breaking and period-doubling bifurcation points. The variation of accuracy is investigated when different number of frequencies are considered.engThis is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier.Journal articlesymmetry-breaking bifurcationperiod-doubling bifurcationhomotopy analysis methodanalytical approximationhttp://dx.doi.org/10.1016/j.cnsns.2014.08.015