Steady-state analysis of a bistable system subject to a coloured multiplicative noise and a white additive noise with coloured cross-correlated noises
Wang Can-Jun (王参军)ab, Chen Shi-Bo (陈世波)a, Mei Dong-Cheng (梅冬成)a
a Department of Physics, Yunnan University, Kunming 650091, China; b Nonlinear Research Institute, Baoji University of Sciences and Arts, Baoji 721007, China
Abstract The steady-state properties of a bistable system are investigated when both the multiplicative noise and the coupling between additive and multiplicative noises are coloured with different values of noise correlation times $\tau_1$ and $\tau_2$. After introducing a dimensionless parameter $R(R=\alpha/D$, $D$ is the intensity of the multiplicative noise and $\alpha$ is the intensity of the additive noise), and performing the numerical computations, we find the following points: (1) For the case of $R>1$, $\lambda$ (the intensity of correlation between additive and multiplicative noises), $\tau_{1}$ and $\tau_{2}$ can induce the stationary probability distribution (SPD) transition from bimodal to unimodal in structure, but for the cases of $R\leq1$, the bimodal structure is preserved; (2) $\alpha$ can also induce the SPD transition from bimodal to unimodal in structure; (3) the bimodal structure of the SPD exhibits a symmetrical structure as $D$ increases.
Received: 28 October 2005
Revised: 11 April 2006
Accepted manuscript online:
Fund: Project supported by the National Nature Science Foundation of China (Grant No 10363001) and the
project of Baoji University of Sciences and Arts of China (Grant No ZK2508).
Cite this article:
Wang Can-Jun (王参军), Chen Shi-Bo (陈世波), Mei Dong-Cheng (梅冬成) Steady-state analysis of a bistable system subject to a coloured multiplicative noise and a white additive noise with coloured cross-correlated noises 2006 Chinese Physics 15 1435
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