Period-Doubling Bifurcation of Stochastic Fractional-Order Duffing System via Chebyshev Polynomial Approximation
Joint Authors
Source
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-04-16
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
Fractional-order calculus is more competent than integer-order one when modeling systems with properties of nonlocality and memory effect.
And many real world problems related to uncertainties can be modeled with stochastic fractional-order systems with random parameters.
Therefore, it is necessary to analyze the dynamical behaviors in those systems concerning both memory and uncertainties.
The period-doubling bifurcation of stochastic fractional-order Duffing (SFOD for short) system with a bounded random parameter subject to harmonic excitation is studied in this paper.
Firstly, Chebyshev polynomial approximation in conjunction with the predictor-corrector approach is used to numerically solve the SFOD system that can be reduced to the equivalent deterministic system.
Then, the global and local analysis of period-doubling bifurcation are presented, respectively.
It is shown that both the fractional-order and the intensity of the random parameter can be taken as bifurcation parameters, which are peculiar to the stochastic fractional-order system, comparing with the stochastic integer-order system or the deterministic fractional-order system.
Moreover, the Chebyshev polynomial approximation is proved to be an effective approach for studying the period-doubling bifurcation of the SFOD system.
American Psychological Association (APA)
Lei, Youming& Wang, Yanyan. 2017. Period-Doubling Bifurcation of Stochastic Fractional-Order Duffing System via Chebyshev Polynomial Approximation. Shock and Vibration،Vol. 2017, no. 2017, pp.1-12.
https://search.emarefa.net/detail/BIM-1204440
Modern Language Association (MLA)
Lei, Youming& Wang, Yanyan. Period-Doubling Bifurcation of Stochastic Fractional-Order Duffing System via Chebyshev Polynomial Approximation. Shock and Vibration No. 2017 (2017), pp.1-12.
https://search.emarefa.net/detail/BIM-1204440
American Medical Association (AMA)
Lei, Youming& Wang, Yanyan. Period-Doubling Bifurcation of Stochastic Fractional-Order Duffing System via Chebyshev Polynomial Approximation. Shock and Vibration. 2017. Vol. 2017, no. 2017, pp.1-12.
https://search.emarefa.net/detail/BIM-1204440
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1204440