Bistable kinetic model driven by correlated noises: Unified colored-noise approximation
Bistable kinetic model driven by correlated noises: Unified colored-noise approximation
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DOI：
10.1103/physreve.52.3228
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发表时间：
1995-09
影响因子：
2.4
通讯作者：
Cao Li;Wu Da–jin;Ke Sheng-zhi
中科院分区：
文献类型：
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作者：
Cao Li;Wu Da–jin;Ke Sheng-zhi
通过扩展的统一有色噪声近似推导出由相关高斯噪声驱动的一般一维非马尔可夫系统的福克-普朗克方程。获得一般平稳概率分布（SPD）。 SPD 包含三个重要的限制：不相关噪声限制、白噪声限制和通常的不相关白噪声限制。上述SPD揭示了以下重要的物理方面。(1)与众所周知的不相关白噪声情况相比，加性噪声参数无法进入SPD的极值方程，现在即使系统由不相关噪声驱动，加性噪声参数也确实作为非马尔可夫效应进入极值方程。(2)当噪声之间确实存在相关性时，SPD包含由噪声的相关性和颜色引起的信息。本简要报告中获得的一般结果适用于双稳态动力学模型。我们发现，对于模型的稳态，在存在相关噪声的情况下，状态变量 x 相对于原点的反射下的 SPD 对称性被破坏。然而，在由不相关噪声驱动的非马尔可夫过程的情况下，上述对称性被保留。
A Fokker-Planck equation for a general one-dimensional non-Markovian system driven by correlated Gaussian noises is derived by means of an extended unified colored-noise approximation. The general stationary probability distribution (SPD) is obtained. The SPD contains three important limits: the uncorrelated noise limit, the white noise limit, and the usual uncorrelated white noise limit. The following important physical aspects have been revealed by virtue of the above-mentioned SPD.(1) In contrast to the well known case of uncorrelated white noises where the parameter of additive noise cannot enter the extremal equation of SPD, now the additive noise parameter does enter the extremal equation as a non-Markovian effect even if the system is driven by uncorrelated noises.(2) When the correlation between the noises does exist, the SPD contains information caused by both correlation and color of the noises. The general results obtained in this Brief Report are applied to a bistable kinetic model. We find for the steady state of the model that in the case of correlated noises, the symmetry of SPD under the reflection of the state variable x with respect to the origin is destroyed. However in the case of non-Markovian processes driven by uncorrelated noises, the above symmetry is preserved.