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Chaotic dynamics of the fractionally damped Duffing equation
Long-Jye Sheu1; Hsien-Keng Chen2; Juhn-Horng Chen1; Lap-Mou Tam3
2007
Source PublicationChaos, Solitons and Fractals
ISSN0960-0779
Volume32Issue:4Pages:1459-1468
Abstract

Vibration phenomena of the fractionally damped systems have attracted increasing attentions in recent years. In this paper, dynamics of the fractionally damped Duffing equation is examined. The fractionally damped Duffing equation is transformed into a set of fractional integral equations solved by a predictor-corrector method. The effect of fractional order of damping on the dynamic behaviors of the motion is the main subject of the study. In this work, bifurcation of the parameter-dependent system is drawn numerically. The time evolutions of the nonlinear dynamical system responses are also described in phase portraits and the Poincaré map technique. In addition, the occurrence and the nature of chaotic attractors are verified by evaluating the largest Lyapunov exponents. Results obtained from this study illustrates that the fractional order of damping has a significant effect on the dynamic behaviors of the motion. The size of the attractor trends to enlarge when fractional order α increases. Regular motions (including period-3 motion) and chaotic motions are examined. Moreover, a period doubling route to chaos is also found. Many period-3 windows are also observed in bifurcation diagram. © 2005 Elsevier Ltd. All rights reserved.

DOIhttp://doi.org/10.1016/j.chaos.2005.11.066
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics ; Physics
WOS SubjectMathematics, Interdisciplinary Applications ; Physics, Multidisciplinary ; Physics, Mathematical
WOS IDWOS:000243776300026
The Source to ArticleScopus
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Citation statistics
Cited Times [WOS]:57   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF ELECTROMECHANICAL ENGINEERING
Corresponding AuthorHsien-Keng Chen
Affiliation1.Department of Mechanical Engineering, Chung Hua University, Hsinchu, Taiwan
2.Department of Industrial Engineering and Management Hsiuping Institute of Technology, No. 11 Gungye Road, Dali City, Taichung, Taiwan
3.Department of Electromechanical Engineering, University of Macau, Macau
Recommended Citation
GB/T 7714
Long-Jye Sheu,Hsien-Keng Chen,Juhn-Horng Chen,et al. Chaotic dynamics of the fractionally damped Duffing equation[J]. Chaos, Solitons and Fractals,2007,32(4):1459-1468.
APA Long-Jye Sheu,Hsien-Keng Chen,Juhn-Horng Chen,&Lap-Mou Tam.(2007).Chaotic dynamics of the fractionally damped Duffing equation.Chaos, Solitons and Fractals,32(4),1459-1468.
MLA Long-Jye Sheu,et al."Chaotic dynamics of the fractionally damped Duffing equation".Chaos, Solitons and Fractals 32.4(2007):1459-1468.
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