The number of limit cycle bifurcation diagrams for the generalized mixed Rayleigh-Liénard oscillator

Q. Ding; A. Y T Leung

doi:10.1016/j.jsv.2008.11.014

Author(s)

Q. Ding
A. Y T Leung

Detail(s)

Original language	English
Pages (from-to)	393-400
Journal / Publication	Journal of Sound and Vibration
Volume	322
Issue number	1-2
Publication status	Published - 24 Apr 2009

Link(s)

DOI	DOI https://doi.org/10.1016/j.jsv.2008.11.014 Final Published version
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Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-61749103686&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(6b86450f-7559-4022-b399-e225a47bf89b).html

Abstract

This paper investigates the generalized mixed Rayleigh-Liénard oscillator with highly nonlinear terms. Not restrict to the number of limit cycles, this analysis considers mainly the number of limit cycle bifurcation diagrams of the system. First, the singularity theory approach is applied to the first-order averaged approximation of the system with lower-order nonlinear terms to reveal all possible bifurcation diagrams. By summarizing the generating rule and structural distinction of different bifurcation diagrams, a numerical procedure is then developed. Calculation suggests that the number of bifurcation diagrams increase very fast as the order of nonlinear terms. Lastly, numerical simulations are adopted to approve the analytical results. © 2008 Elsevier Ltd. All rights reserved.

Citation Format(s)

[ RIS ] [ BibTeX ]

The number of limit cycle bifurcation diagrams for the generalized mixed Rayleigh-Liénard oscillator. / Ding, Q.; Leung, A. Y T.
In: Journal of Sound and Vibration, Vol. 322, No. 1-2, 24.04.2009, p. 393-400.

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

Ding, Q & Leung, AYT 2009, 'The number of limit cycle bifurcation diagrams for the generalized mixed Rayleigh-Liénard oscillator', Journal of Sound and Vibration, vol. 322, no. 1-2, pp. 393-400. https://doi.org/10.1016/j.jsv.2008.11.014

Ding, Q., & Leung, A. Y. T. (2009). The number of limit cycle bifurcation diagrams for the generalized mixed Rayleigh-Liénard oscillator. Journal of Sound and Vibration, 322(1-2), 393-400. https://doi.org/10.1016/j.jsv.2008.11.014

Ding Q, Leung AYT. The number of limit cycle bifurcation diagrams for the generalized mixed Rayleigh-Liénard oscillator. Journal of Sound and Vibration. 2009 Apr 24;322(1-2):393-400. doi: 10.1016/j.jsv.2008.11.014

Ding, Q. ; Leung, A. Y T. / The number of limit cycle bifurcation diagrams for the generalized mixed Rayleigh-Liénard oscillator. In: Journal of Sound and Vibration. 2009 ; Vol. 322, No. 1-2. pp. 393-400.