Fractional noise destroys or induces a stochastic bifurcation

Journal Article · Sun Dec 15 00:00:00 EST 2013 · Chaos (Woodbury, N. Y.)

DOI:https://doi.org/10.1063/1.4830271· OSTI ID:22251910

Yang, Qigui ^[1]; Zeng, Caibin ^[1]; Wang, Cong ^[2]

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1. School of Sciences, South China University of Technology, Guangzhou 510640 (China)
2. School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640 (China)

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.

• OSTI ID: 22251910
• Journal Information: Chaos (Woodbury, N. Y.), Vol. 23, Issue 4; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 1054-1500
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BIFURCATION
BROWNIAN MOVEMENT
MARKOV PROCESS
NOISE