中国物理B ›› 2006, Vol. 15 ›› Issue (7): 1435-1440.doi: 10.1088/1009-1963/15/7/009

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Steady-state analysis of a bistable system subject to a coloured multiplicative noise and a white additive noise with coloured cross-correlated noises

陈世波1, 梅冬成1, 王参军2   

  1. (1)Department of Physics, Yunnan University, Kunming 650091, China; (2)Department of Physics, Yunnan University, Kunming 650091, China；Nonlinear Research Institute, Baoji University of Sciences and Arts, Baoji 721007, China
  • 收稿日期:2005-10-28 修回日期:2006-04-11 出版日期:2006-07-20 发布日期:2006-07-20
  • 基金资助:
    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).

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   

  1. a Department of Physics, Yunnan University, Kunming 650091, China; b Nonlinear Research Institute, Baoji University of Sciences and Arts, Baoji 721007, China
  • Received:2005-10-28 Revised:2006-04-11 Online:2006-07-20 Published:2006-07-20
  • Supported by:
    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).

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摘要： 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.

关键词: bistable system, correlated noise, stationary probability distribution

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.

Key words: bistable system, correlated noise, stationary probability distribution

中图分类号:  (Noise)

  • 05.40.Ca
02.50.Cw (Probability theory) 02.50.Ng (Distribution theory and Monte Carlo studies)