Grazing bifurcations of initially quasi-periodic system attractors

Harry J. Dankowicz, Petri T. Piiroinen, Arne B. Nordmark

Research output: Contribution to conferencePaperpeer-review


This paper discusses the dramatic changes in system dynamics that arise as parameter variations lead to the appearance of grazing intersections between periodic and quasi-periodic attractors and state-space discontinuities. In particular, a method based on the discontinuity-mapping approach is employed to predict the effects of near-grazing interactions with the discontinuity surface solely based on information about the discontinuity and the pre-grazing trajectory and requiring no knowledge of the impacting system. An example from the study of legged locomotion is used to illustrate the significance of such grazing bifurcations on the presence of sustained gait in simple anthropomorphic mechanisms. The predictive power of the discontinuity-mapping approach is illustrated on a low-dimensional model example.

Original languageEnglish (US)
Number of pages7
StatePublished - 2001
Externally publishedYes
Event18th Biennial Conference on Mechanical Vibration and Noise - Pittsburgh, PA, United States
Duration: Sep 9 2001Sep 12 2001


Other18th Biennial Conference on Mechanical Vibration and Noise
Country/TerritoryUnited States
CityPittsburgh, PA

ASJC Scopus subject areas

  • Modeling and Simulation
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design


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