Chaotic thresholds for the piecewise linear discontinuous system with multiple well potentials

Yanwei Han, Qingjie Cao*, Yushu Chen, Marian Wiercigroch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


In this paper we investigate the bifurcations and the chaos of a piecewise linear discontinuous (PWLD) system based upon a rig-coupled SD oscillator, which can be smooth or discontinuous (SD) depending on the value of a system parameter, proposed in [18], showing the equilibrium bifurcations and the transitions between single, double and triple well dynamics for smooth regions. All solutions of the perturbed PWLD system, including equilibria, periodic orbits and homoclinic-like and heteroclinic-like orbits, are obtained and also the chaotic solutions are given analytically for this system. This allows us to employ the Melnikov method to detect the chaotic criterion analytically from the breaking of the homoclinic-like and heteroclinic-like orbits in the presence of viscous damping and an external harmonic driving force. The results presented here in this paper show the complicated dynamics for PWLD system of the subharmonic solutions, chaotic solutions and the coexistence of multiple solutions for the single well system, double well system and the triple well dynamics. (C) 2014 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)145-152
Number of pages8
JournalInternational Journal of Non-Linear Mechanics
Early online date21 Sept 2014
Publication statusPublished - Apr 2015

Bibliographical note

Date of Acceptance: 14/06/2014

This project was supported by the National Natural Science Foundation of China Grant No. 11372082 and the National Basic Research Program of China Grant No. 2015CB057405.


  • SD oscillator
  • PWLD system
  • Homoclinic-like orbit
  • Heteroclinic-like orbit
  • Melnikov method
  • archetypal oscillator
  • dynamics
  • smooth
  • bifurcations


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