Paper Info
Title
Stochastic P-Bifurcation Analysis of Fractional Smooth and Discontinuous Oscillator with an Extended Fast Method
Abstract
In this paper, stochastic bifurcations of a fractional-order smooth and discontinuous (SD) oscillator composed of different viscoelastic materials are studied. As a widely applicable algorithm for various fractional-orders cases, an extended fast algorithm is introduced to obtain the statistics of the response, where the fractional derivative is separated into a history part and a local part with a predetermined memory length. The local part is approximated by a highly accurate algorithm while the history part is computed by an efficient convolution algorithm. Through this accurate and fast method, effects of the system parameters on the dynamic behaviors, such as the fractional order, smoothness parameter, and frequency of harmonic force, are thus successfully investigated. Abundant stochastic P-bifurcation phenomena are discussed in detail. Further, it is found that only when the damping material shows nearly elastic behaviors, the probability density functions of the system exhibit the crater shape. Experiments show that the fast algorithm is accurate for different fractional orders.
Year
DOI
Venue
2022
10.1142/S0218127422500973
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Keywords
DocType
Volume
Fractional derivative, smooth and discontinuous oscillator, extended fast method, stochastic P-bifurcation
Journal
32
Issue
ISSN
Citations 
07
0218-1274
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Minjuan Yuan100.34
Liang Wang24317243.28
Yiyu Jiao300.34
Wei Xu4411.47