Period-Doubling Bifurcation of Stochastic Fractional-Order Duffing System via Chebyshev Polynomial Approximation

• Published in: Shock and vibration Vol. 2017; no. 2017; pp. 1 - 12
• Main Authors: Lei, Youming, Wang, Yanyan
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 01.01.2017; Hindawi; John Wiley & Sons, Inc; Wiley
• Subjects: Algorithms; Bifurcation theory; Chebyshev approximation; Mathematical research; Stochastic models; Studies
• ISSN: 1070-9622; 1875-9203
• DOI: 10.1155/2017/4162363

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.