Control of Bistability in a Delayed Duffing Oscillator
Joint Authors
Belhaq, Mohamed
Hamdi, Mustapha
Source
Advances in Acoustics and Vibration
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-5, 5 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-12-21
Country of Publication
Egypt
No. of Pages
5
Main Subjects
Abstract EN
The effect of a high-frequency excitation on nontrivial solutions and bistability in a delayed Duffing oscillator with a delayed displacement feedback is investigated in this paper.
We use the technique of direct partition of motion and the multiple scales method to obtain the slow dynamic of the system and its slow flow.
The analysis of the slow flow provides approximations of the Hopf and secondary Hopf bifurcation curves.
As a result, this study shows that increasing the delay gain, the system undergoes a secondary Hopf bifurcation.
Further, it is indicated that as the frequency of the excitation is increased, the Hopf and secondary Hopf bifurcation curves overlap giving birth in the parameter space to small regions of bistability where a stable trivial steady state and a stable limit cycle coexist.
Numerical simulations are carried out to validate the analytical finding.
American Psychological Association (APA)
Hamdi, Mustapha& Belhaq, Mohamed. 2011. Control of Bistability in a Delayed Duffing Oscillator. Advances in Acoustics and Vibration،Vol. 2012, no. 2012, pp.1-5.
https://search.emarefa.net/detail/BIM-505117
Modern Language Association (MLA)
Hamdi, Mustapha& Belhaq, Mohamed. Control of Bistability in a Delayed Duffing Oscillator. Advances in Acoustics and Vibration No. 2012 (2012), pp.1-5.
https://search.emarefa.net/detail/BIM-505117
American Medical Association (AMA)
Hamdi, Mustapha& Belhaq, Mohamed. Control of Bistability in a Delayed Duffing Oscillator. Advances in Acoustics and Vibration. 2011. Vol. 2012, no. 2012, pp.1-5.
https://search.emarefa.net/detail/BIM-505117
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-505117