title: Fractional noise destroys or induces a stochastic bifurcation.
abstract: Little seems to be known about the stochastic bifurcation phenomena of non-Markovian systems. Our intention in this paper is to understand such complex dynamics by a simple system, namely, the Black-Scholes model driven by a mixed fractional Brownian motion. The most interesting finding is that the multiplicative fractional noise not only destroys but also induces a stochastic bifurcation under some suitable conditions. So it opens a possible way to explore the theory of stochastic bifurcation in the non-Markovian framework.
authors.affiliation: School of Sciences, South China University of Technology, Guangzhou 510640, People's Republic of China.
authors.forename: Qigui
authors.initials: Q
authors.lastname: Yang
authors.affiliation: School of Sciences, South China University of Technology, Guangzhou 510640, People's Republic of China.
authors.forename: Caibin
authors.initials: C
authors.lastname: Zeng
authors.affiliation: School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640, People's Republic of China.
authors.forename: Cong
authors.initials: C
authors.lastname: Wang
mesh_terms: D008962:Models, Theoretical; D059629:Signal-To-Noise Ratio; D013269:Stochastic Processes