Subcritical Hopf bifurcation in the delay equation model for machine tool vibrations

Tamás Kalmár-Nagy, Gábor Stépán, Francis C. Moon

Research output: Contribution to journalArticle

194 Citations (Scopus)


We show the existence of a subcritical Hopf bifurcation in the delay-differential equation model of the so-called regenerative machine tool vibration. The calculation is based on the reduction of the infinite-dimensional problem to a two-dimensional center manifold. Due to the special algebraic structure of the delayed terms in the nonlinear part of the equation, the computation results in simple analytical formulas. Numerical simulations gave excellent agreement with the results.

Original languageEnglish
Pages (from-to)121-142
Number of pages22
JournalNonlinear Dynamics
Issue number2
Publication statusPublished - Oct 1 2001


  • Center manifold
  • Chatter
  • Delay differential equation
  • Hopf bifurcation

ASJC Scopus subject areas

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

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