Bifurcation analysis of a piecewise-linear impact oscillator with drift

Joseph Paez Chavez*, Ekaterina Pavlovskaia, Marian Wiercigroch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

56 Citations (Scopus)


We investigate the complex bifurcation scenarios occurring in the dynamic response of a piecewise-linear impact oscillator with drift, which is able to describe qualitatively the behaviour of impact drilling systems. This system has been extensively studied by numerical and analytical methods in the past, but its intricate bifurcation structure has largely remained unknown. For the bifurcation analysis, we use the computational package TC-HAT, a toolbox of AUTO 97 for numerical continuation and bifurcation detection of periodic orbits of non-smooth dynamical systems (Thota and Dankowicz, SIAM J Appl Dyn Syst 7(4):1283-322, 2008) The study reveals the presence of co-dimension-1 and -2 bifurcations, including fold, period-doubling, grazing, flip-grazing, fold-grazing and double grazing bifurcations of limit cycles, as well as hysteretic effects and chaotic behaviour. Special attention is given to the study of the rate of drift, and how it is affected by the control parameters.

Original languageEnglish
Pages (from-to)213-227
Number of pages15
JournalNonlinear Dynamics
Issue number1-2
Early online date22 Feb 2014
Publication statusPublished - Jul 2014

Bibliographical note

Acknowledgments The authors wish to thank Scottish Enterprise
for the financial support to this research.

Nonlinear Dynamics July 2014, Volume 77, Issue 1, pp 229–230
Erratum to: Bifurcation analysis of a piecewise-linear impact oscillator with drift
DOI: 10.1007/s11071-014-1358-5


  • drifting impact oscillator
  • non-smooth dynamical system
  • bifurcation analysis
  • numerical continuation
  • TC-HAT
  • resonance enhanced drilling
  • discontinuity-induced bifurcations
  • frictional slider
  • dynamical-systems
  • model
  • regimes
  • cycles


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