Stochastic bifurcations of a fractional-order vibro-impact system driven by additive and multiplicative Gaussian white noises
type: Item
instance of: scholarly article
title: Stochastic bifurcations of a fractional-order vibro-impact system driven by additive and multiplicative Gaussian white noises
zbMATH Open document ID: 1477.34085
DOI: 10.1155/2019/6737139
author: Yongge Yang
author: Yahui Sun
author: Wei Xu
published in: Complexity
publication date: 2019-11-25T00:00:00Z
review text: It has been revealed that several natural systems are explained with differential fractional-order equations, where a fractional derivative order is utilized. As the stochastic disturbances are inevitable such as strong winds, earthquakes, and ocean waves, in recent years, stochastic differential fractional-order equations have become more and more important and stimulating to researchers due to their successful and possible applications in numerous arenas. Vibro-impact systems are used broadly in modelling machine dynamics, vibration engineering, and structural mechanics. Study of vibro-impact systems requires the investigation of mathematical models with discontinuities and shows their behaviour as intensely non-linear. The debate on the stochastic systems with both vibro-impact factors and fractional derivative element is uncommon. This paper is involved with the stochastic bifurcation of a fractional-order vibro-impact system powered by additive and multiplicative Gaussian white noises. There are two challenges to study the stationary response of the fractional vibro-impact systems under Gaussian white noises. The first one is how to deal with the discontinuity of the original system. The second one is how to get the explicit expression of the averaged drift coefficient when we utilize the stochastic averaging method. These two challenges have been solved in this paper by the non-smooth transformations and stochastic averaging method.
reviewed by: Seifedine Kadry
Mathematics Subject Classification ID: 34F10
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 7136332
zbMATH Keywords: fractional derivative
zbMATH Keywords: bifurcations
zbMATH Keywords: random process
zbMATH Keywords: stochastic fractional-order systems
zbMATH Keywords: vibro-impact factors
zbMATH Keywords: white noise
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2019/6737139
OpenAlex ID: W2982306372
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description: scientific article; zbMATH DE number 7136332