Volume 3, Issue 2, June 2018, Page: 34-50
Chaotic Dynamics of an Extended Duffing Oscillator Under Periodic Excitation
Hervé Lucas Koudahoun, Department of Physics, University of Abomey-Calavi, Abomey-Calavi, Benin
Yélomè Judicaël Fernando Kpomahou, Department of Industrial and Technical Sciences, University of Abomey, Abomey, Benin
Jean Akande, Department of Physics, University of Abomey-Calavi, Abomey-Calavi, Benin
Damien Kêgnidé Kolawolé Adjaï, Department of Physics, University of Abomey-Calavi, Abomey-Calavi, Benin
Received: Jun. 29, 2018;       Accepted: Jul. 12, 2018;       Published: Aug. 6, 2018
DOI: 10.11648/j.wjap.20180302.13      View  309      Downloads  26
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.
Keywords
Extended Duffing Oscillator, Resonance States, Stability, Limit Cycles, Bifurcation and Jump Phenomena, Periodic and Quasi-periodic Oscillations, Chaos
To cite this article
Hervé Lucas Koudahoun, Yélomè Judicaël Fernando Kpomahou, Jean Akande, Damien Kêgnidé Kolawolé Adjaï, Chaotic Dynamics of an Extended Duffing Oscillator Under Periodic Excitation, World Journal of Applied Physics. Vol. 3, No. 2, 2018, pp. 34-50. doi: 10.11648/j.wjap.20180302.13
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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