Bifurcation of a duffing oscillator having nonlinear fractional derivative feedback

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

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  • A. Y T Leung
  • H. X. Yang
  • P. Zhu


Original languageEnglish
Article number1450028
Journal / PublicationInternational Journal of Bifurcation and Chaos
Issue number3
Publication statusPublished - Mar 2014


Active feedback control is commonly used to attenuate undesired vibrations in vibrating machineries and structures, such as bridges, highways and aircrafts. In this paper, we investigate the primary resonance and 1/3 subharmonic resonance of a harmonically forced Duffing oscillator under fractional nonlinear feedback control. By means of the first order averaging method, slow flow equations governing the modulations of amplitude and phase of the oscillator are obtained. An approximate solution for the steady state periodic response is derived and its stability is determined by the Routh-Hurwitz criterion. We demonstrate that appropriate choices on the control strategies and feedback gains can delay or eliminate the undesired bifurcations and reduce the amplitude peak both of the primary and subharmonic resonances. Analytical results are verified by comparisons with the numerical integration results. © 2014 World Scientific Publishing Company.

Research Area(s)

  • Duffing oscillator, feedback control, fractional derivative, resonant response