Semi-analytical method to study piecewise linear oscillators

Agustín Hernández Rocha, Damián H. Zanette, Marian Wiercigroch

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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
Article number107193
Number of pages20
JournalCommunications in Nonlinear Science and Numerical Simulation
Early online date13 Mar 2023
Publication statusPublished - 15 Jun 2023

Bibliographical note

The authors would like to thank the Balseiro Institute and the National Commission
of Atomic Energy for the support. In particular, financial support for the Invited Professor Programme of the Balseiro Institute, which made international collaboration possible.

Data Availability Statement

No data was used for the research described in the article.


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


Dive into the research topics of 'Semi-analytical method to study piecewise linear oscillators'. Together they form a unique fingerprint.

Cite this