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Mathematical Problems in Engineering
Volume 2014, Article ID 678976, 6 pages
http://dx.doi.org/10.1155/2014/678976
Research Article

Impact of Correlated Noises on Additive Dynamical Systems

1School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
2Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA

Received 14 April 2014; Accepted 4 August 2014; Published 3 September 2014

Academic Editor: Wuquan Li

Copyright © 2014 Chujin Li and Jinqiao Duan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Impact of correlated noises on dynamical systems is investigated by considering Fokker-Planck type equations under the fractional white noise measure, which correspond to stochastic differential equations driven by fractional Brownian motions with the Hurst parameter . Firstly, by constructing the fractional white noise framework, one small noise limit theorem is proved, which provides an estimate for the deviation of random solution orbits from the corresponding deterministic orbits. Secondly, numerical experiments are conducted to examine the probability density evolutions of two special dynamical systems, as the Hurst parameter varies. Certain behaviors of the probability density functions are observed.