Threshold for Chaos of a Duffing Oscillator with Fractional-Order Derivative
Joint Authors
Xing, Wuce
Chen, Enli
Chang, Yujian
Wang, Meiqi
Source
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-08-27
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
In this paper, the necessary condition for the chaotic motion of a Duffing oscillator with the fractional-order derivative under harmonic excitation is investigated.
The necessary condition for the chaos in the sense of Smale horseshoes is established based on the Melnikov method, and then the chaotic threshold curve is obtained.
The largest Lyapunov exponents are provided, and some other typical numerical simulation results, including the time histories, frequency spectrograms, phase portraits, and Poincare maps, are presented and compared.
From the analysis of the numerical simulation results, it could be found that, near the chaotic threshold curve, the system generates chaos via the period-doubling bifurcation, from single periodic motion to period-2 motion and period-4 motion to chaotic motion.
The effects of fractional-order parameters, the stiffness coefficient, and the damping coefficient on the threshold value of the chaotic motion are analytically discussed.
The results show that the coefficient of the fractional-order derivative has great effect on the threshold value of the chaotic motion, while the order of the fractional-order derivative has less.
The analysis results reveal some new phenomena, and it could be useful for designing or controlling dynamic systems with the fractional-order derivative.
American Psychological Association (APA)
Xing, Wuce& Chen, Enli& Chang, Yujian& Wang, Meiqi. 2019. Threshold for Chaos of a Duffing Oscillator with Fractional-Order Derivative. Shock and Vibration،Vol. 2019, no. 2019, pp.1-16.
https://search.emarefa.net/detail/BIM-1210905
Modern Language Association (MLA)
Xing, Wuce…[et al.]. Threshold for Chaos of a Duffing Oscillator with Fractional-Order Derivative. Shock and Vibration No. 2019 (2019), pp.1-16.
https://search.emarefa.net/detail/BIM-1210905
American Medical Association (AMA)
Xing, Wuce& Chen, Enli& Chang, Yujian& Wang, Meiqi. Threshold for Chaos of a Duffing Oscillator with Fractional-Order Derivative. Shock and Vibration. 2019. Vol. 2019, no. 2019, pp.1-16.
https://search.emarefa.net/detail/BIM-1210905
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1210905