An efficient method for switching branches of period-doubling bifurcations of strongly non-linear autonomous oscillators with many degrees of freedom

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)787-808
Journal / PublicationJournal of Sound and Vibration
Volume267
Issue number4
Publication statusPublished - 30 Oct 2003

Abstract

Popular algorithms for switching branches at a bifurcation point of strongly non-linear oscillators are generally quite involved as they require the computation of the tangent of a new branch and second derivatives. In this paper, a simple but efficient algorithm is presented by using a perturbation-incremental method for switching branches at a period-doubling bifurcation of strongly non-linear autonomous oscillators with many degrees of freedom. To switch to a new branch at a bifurcation point, a parameter is simply turned on from zero to a small positive value so as to obtain an initial solution on the emanating branch for subsequent continuation, The parametric value at a period-doubling bifurcation can also be determined accurately. Furthermore, limit cycles of period 2k (k≥1) can be calculated to any desired degree of accuracy. © 2002 Elsevier Science Ltd. All rights reserved.

Citation Format(s)

An efficient method for switching branches of period-doubling bifurcations of strongly non-linear autonomous oscillators with many degrees of freedom. / Chung, K. W.; Chan, C. L.; Xu, J.
In: Journal of Sound and Vibration, Vol. 267, No. 4, 30.10.2003, p. 787-808.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review