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

Yanwei Han, Qingjie Cao, Yushu Chen, Marian Wiercigroch

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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
Volume70
Early online date21 Sep 2014
DOIs
Publication statusPublished - Apr 2015

Keywords

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

Cite this

Chaotic thresholds for the piecewise linear discontinuous system with multiple well potentials. / Han, Yanwei; Cao, Qingjie; Chen, Yushu; Wiercigroch, Marian.

In: International Journal of Non-Linear Mechanics, Vol. 70, 04.2015, p. 145-152.

Research output: Contribution to journalArticle

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abstract = "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.",
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AB - 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.

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