关联噪声和周期信号驱动的非对称双稳系统的稳态分析

J4 ›› 2014, Vol. 31 ›› Issue (1): 86-93.

关联噪声和周期信号驱动的非对称双稳系统的稳态分析

王国威¹,程庆华²,徐大海¹

长江大学物理科学与技术学院，湖北荆州 434023

收稿日期:2013-05-08 修回日期:2013-05-29 出版日期:2014-01-28 发布日期:2013-12-31
通讯作者: 程庆华（1957-），女，湖北人，教授，从事激光物理与技术的研究和教学。 E-mail:qhcheng@yangtzeu.edu.cn
作者简介:王国威（1987-）湖北人，研究生，从事激光物理的研究。E-mail：gwwang2009@sina.com
基金资助:
湖北省教育厅重点科学技术研究项目(D20121203)资助

Steady-state analysis of an asymmetric bistable system driven by cross-correlated noises with periodic signal

WANG Guo-wei, CHENG Qing-hua, XU Da-hai

College of Physics Sinence and Technology, Yangtze University , Jingzhou 434023，China

Received:2013-05-08 Revised:2013-05-29 Published:2014-01-28 Online:2013-12-31

摘要/Abstract

摘要： 运用Liouville equation和诺维科夫原理,解出了关联噪声和周期信号共同驱动的非对称双稳系统的近似福克-普朗克方程,并求解了其稳态概率密度函数.在此基础上,分析了乘性噪声强度、加性噪声强度、噪声间关联系数 ,周期信号振幅、频率以及系统非对称参数等对稳态概率密度分布曲线的影响.结果表明:(1)噪声强度及其关联、周期信号振幅、系统非对称参数的改变均能引起稳态概率密度分布曲线单峰结构和双峰结构之间的转换,即能够诱导非平衡相变产生；(2)周期信号频率改变时,没有非平衡相变发生；(3)当系统非对称参数为零时,稳态概率密度分布曲线具有关于的对称结构；当系统非对称参数不等于零时,其对称结构被破坏.

关键词: 非线性光学, 非对称双稳系统, 福克-普朗克方程, 噪声, 稳态概率密度

Abstract: The stationary probability distribution (SPD) is investigated in an asymmetric bistable system driven by cross-correlated multiplicative white noise and additive white noise with periodic signal. By virtue of the Liouville Equation and Novikov Theorem, the approximate Fokker-Planck equation is derived, and the analytic expressions of the stationary probability is obtained. The results indicate that related parameters, including the asymmetric parameter, the amplitude of periodic signal, the intensities of the noises and the intensity of correlation between multiplicative noise and additive noise, can induce the SPD transition from bimodal to unimodal in structure. Furthermore, the structure of the SPD exhibits a symmetrical structure at when .But the symmetry of SPD at is destroyed when .

Key words: nonlinear optics, asymmetric bistable system, Fokker-Planck equation, noise, stationary probability distribution

中图分类号:

O431.2

王国威程庆华徐大海. 关联噪声和周期信号驱动的非对称双稳系统的稳态分析[J]. J4, 2014, 31(1): 86-93.

WANG Guo-wei, CHENG Qing-hua, XU Da-hai. Steady-state analysis of an asymmetric bistable system driven by cross-correlated noises with periodic signal[J]. J4, 2014, 31(1): 86-93.

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