In this paper, chaotic dynamics of a cubic-quintic-septic Duffing oscillator subjected to periodic excitation is investigated. The multiple scales method is used to determine the various resonance states of the model. It is found that the considered model posses thirteen resonance states whose seven are thoroughly studied. The steady-state solutions and theirs stabilities are determined. The frequency-amplitude curves show that the considered system presents mixed behavior, limit cycles, hysteresis, jump and bifurcation phenomena. It is also noticed that these phenomena are strongly influenced by quintic-septic nonlinearity and excitation amplitude. Bifurcation structures displayed by the model for each considered type of resonant states are investigated numerically using the fourth-order Runge-Kutta algorithm. As results, the quintic-septic nonlinearity, linear dissipation and excitation amplitude can be used to control the chaotic behavior of the system.
| Published in | World Journal of Applied Physics (Volume 3, Issue 2) |
| DOI | 10.11648/j.wjap.20180302.13 |
| Page(s) | 34-50 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2018. Published by Science Publishing Group |
Extended Duffing Oscillator, Resonance States, Stability, Limit Cycles, Bifurcation and Jump Phenomena, Periodic and Quasi-periodic Oscillations, Chaos
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APA Style
Hervé Lucas Koudahoun, Yélomè Judicaël Fernando Kpomahou, Jean Akande, Damien Kêgnidé Kolawolé Adjaï. (2018). Chaotic Dynamics of an Extended Duffing Oscillator Under Periodic Excitation. World Journal of Applied Physics, 3(2), 34-50. https://doi.org/10.11648/j.wjap.20180302.13
ACS Style
Hervé Lucas Koudahoun; Yélomè Judicaël Fernando Kpomahou; Jean Akande; Damien Kêgnidé Kolawolé Adjaï. Chaotic Dynamics of an Extended Duffing Oscillator Under Periodic Excitation. World J. Appl. Phys. 2018, 3(2), 34-50. doi: 10.11648/j.wjap.20180302.13
AMA Style
Hervé Lucas Koudahoun, Yélomè Judicaël Fernando Kpomahou, Jean Akande, Damien Kêgnidé Kolawolé Adjaï. Chaotic Dynamics of an Extended Duffing Oscillator Under Periodic Excitation. World J Appl Phys. 2018;3(2):34-50. doi: 10.11648/j.wjap.20180302.13
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Download@article{10.11648/j.wjap.20180302.13,
author = {Hervé Lucas Koudahoun and Yélomè Judicaël Fernando Kpomahou and Jean Akande and Damien Kêgnidé Kolawolé Adjaï},
title = {Chaotic Dynamics of an Extended Duffing Oscillator Under Periodic Excitation},
journal = {World Journal of Applied Physics},
volume = {3},
number = {2},
pages = {34-50},
doi = {10.11648/j.wjap.20180302.13},
url = {https://doi.org/10.11648/j.wjap.20180302.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.wjap.20180302.13},
abstract = {In this paper, chaotic dynamics of a cubic-quintic-septic Duffing oscillator subjected to periodic excitation is investigated. The multiple scales method is used to determine the various resonance states of the model. It is found that the considered model posses thirteen resonance states whose seven are thoroughly studied. The steady-state solutions and theirs stabilities are determined. The frequency-amplitude curves show that the considered system presents mixed behavior, limit cycles, hysteresis, jump and bifurcation phenomena. It is also noticed that these phenomena are strongly influenced by quintic-septic nonlinearity and excitation amplitude. Bifurcation structures displayed by the model for each considered type of resonant states are investigated numerically using the fourth-order Runge-Kutta algorithm. As results, the quintic-septic nonlinearity, linear dissipation and excitation amplitude can be used to control the chaotic behavior of the system.},
year = {2018}
}
TY - JOUR T1 - Chaotic Dynamics of an Extended Duffing Oscillator Under Periodic Excitation AU - Hervé Lucas Koudahoun AU - Yélomè Judicaël Fernando Kpomahou AU - Jean Akande AU - Damien Kêgnidé Kolawolé Adjaï Y1 - 2018/08/06 PY - 2018 N1 - https://doi.org/10.11648/j.wjap.20180302.13 DO - 10.11648/j.wjap.20180302.13 T2 - World Journal of Applied Physics JF - World Journal of Applied Physics JO - World Journal of Applied Physics SP - 34 EP - 50 PB - Science Publishing Group SN - 2637-6008 UR - https://doi.org/10.11648/j.wjap.20180302.13 AB - In this paper, chaotic dynamics of a cubic-quintic-septic Duffing oscillator subjected to periodic excitation is investigated. The multiple scales method is used to determine the various resonance states of the model. It is found that the considered model posses thirteen resonance states whose seven are thoroughly studied. The steady-state solutions and theirs stabilities are determined. The frequency-amplitude curves show that the considered system presents mixed behavior, limit cycles, hysteresis, jump and bifurcation phenomena. It is also noticed that these phenomena are strongly influenced by quintic-septic nonlinearity and excitation amplitude. Bifurcation structures displayed by the model for each considered type of resonant states are investigated numerically using the fourth-order Runge-Kutta algorithm. As results, the quintic-septic nonlinearity, linear dissipation and excitation amplitude can be used to control the chaotic behavior of the system. VL - 3 IS - 2 ER -
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