On the purposeful coarsening of smooth vector fields

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This paper argues for the possibility of purposely approximating smooth vector fields with highly localized variability in terms of piecewise smooth vector fields for the purpose of analyzing the bifurcation characteristics of the corresponding dynamical systems. Here, emphasis is placed on the changes in system response that result as a periodic trajectory begins to incorporate a brief flow segment in the region of high variability under variations in some system parameter. In particular, it is shown that tools from the theory of grazing bifurcations in piecewise-smooth systems may be employed to qualitatively predict the bifurcation scenario associated with such a transition both in terms of the shape of the branch of periodic trajectories and in terms of the persistence of a local attractor in the vicinity of the original periodic trajectory.

Original languageEnglish (US)
Pages (from-to)511-522
Number of pages12
JournalNonlinear Dynamics
Issue number3
StatePublished - Nov 2007


  • Bifurcation analysis
  • Coarsening
  • Grazing bifurcations
  • Piecewise-smooth dynamical systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering


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