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 language | English |
|---|---|
| Pages (from-to) | 145-152 |
| Number of pages | 8 |
| Journal | International Journal of Non-Linear Mechanics |
| Volume | 70 |
| Early online date | 21 Sep 2014 |
| DOIs | |
| Publication status | Published - 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 journal › Article
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TY - JOUR
T1 - Chaotic thresholds for the piecewise linear discontinuous system with multiple well potentials
AU - Han, Yanwei
AU - Cao, Qingjie
AU - Chen, Yushu
AU - Wiercigroch, Marian
N1 - Date of Acceptance: 14/06/2014 Acknowledgments 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.
PY - 2015/4
Y1 - 2015/4
N2 - 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.
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.
KW - SD oscillator
KW - PWLD system
KW - Homoclinic-like orbit
KW - Heteroclinic-like orbit
KW - Melnikov method
KW - archetypal oscillator
KW - dynamics
KW - smooth
KW - bifurcations
U2 - 10.1016/j.ijnonlinmec.2014.09.007
DO - 10.1016/j.ijnonlinmec.2014.09.007
M3 - Article
VL - 70
SP - 145
EP - 152
JO - International Journal of Non-Linear Mechanics
JF - International Journal of Non-Linear Mechanics
SN - 0020-7462
ER -