Semi-analytical method to study piecewise linear oscillators

Agustín Hernández Rocha, Damián H. Zanette, Marian Wiercigroch

Research output: Contribution to journalArticlepeer-review


This article proposes a semi-analytical method to investigate the dynamics and
bifurcation scenarios of piecewise linear oscillators. The method is based on a mapping technique with a matrix structure that allows easy and rapid construction of any periodic orbit. When validated against direct numerical integration simulations, a good correlation and an accurate prediction of bifurcation phenomena were shown. The method is applied to analyze the nonlinear dynamic responses and bifurcations scenarios causes by changes of stiffness and viscous damping. A set of minimum conditions that the system must meet to present period doubling bifurcations and sub-harmonic orbits was given.
Original languageEnglish
JournalCommunications in Nonlinear Science and Numerical Simulation
Publication statusAccepted/In press - 21 Feb 2023


  • Piecewise linear oscillator
  • Semi-analytical solution
  • numerical simulation
  • non-linear dynamics analysis


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