Analysis of grazing bifurcations of quasiperiodic system attractors

Phanikrishna Thota, Harry Dankowicz

Research output: Contribution to journalArticlepeer-review


This paper presents the first application of the discontinuity-mapping approach to the study of near-grazing bifurcations of originally quasiperiodic, co-dimension-two system attractors. The paper establishes an exact formulation for the discontinuity-mapping methodology under the assumption that a Poincaré section can be found that is everywhere transversal to the grazing attractor. In particular, it is shown that, while a reduced formulation may be employed successfully in the case of co-dimension-one attractors, it fails to capture dynamics in directions transversal to the original quasiperiodic attractor. This shortcoming necessitates the full machinery presented here. The generality of the proposed approach is illustrated through numerical analysis of two nonlinear dynamical systems of dimension three and four.

Original languageEnglish (US)
Pages (from-to)163-174
Number of pages12
JournalPhysica D: Nonlinear Phenomena
Issue number2
StatePublished - Aug 15 2006


  • Discontinuity mappings
  • Discontinuity-induced bifurcations
  • Grazing bifurcations
  • Piecewise smooth dynamical systems
  • Quasiperiodic attractors

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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