Variational Superposed Gaussian Approximation for Time-dependent Solutions of Langevin Equations
Variational Superposed Gaussian Approximation for Time-dependent Solutions of Langevin Equations
复制标题
朗之万方程瞬态解的变分叠加高斯近似
DOI：
10.1103/physreve.91.042912
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发表时间：
2015
影响因子：
2.4
通讯作者：
Yoshihiko Hasegawa
中科院分区：
文献类型：
--
作者：
Y. Okamura;M. Kawasaki;Y. Tokura (9/9);Yoshihiko Hasegawa
我们提出了一种变分叠加高斯近似（VSGA），用于受应用信号影响的朗之万方程的动态解，通过变分原理确定叠加高斯分布的时间相关参数。我们将所提出的 VSGA 应用于无法采用传统傅里叶方法的混沌信号驱动的系统，并计算概率密度函数（PDF）和矩的时间演化。白色和彩色高斯噪声项都包含在内以描述波动。我们的计算表明，VSGA 获得的时间相关 PDF 与蒙特卡罗模拟获得的结果非常一致。混沌输入信号和平均响应之间的相关性也被计算为噪声强度的函数，这证实了白噪声和有色噪声都发生了非周期性随机共振。
We propose a variational superposed Gaussian approximation (VSGA) for dynamical solutions of Langevin equations subject to applied signals, determining time-dependent parameters of superposed Gaussian distributions by the variational principle. We apply the proposed VSGA to systems driven by a chaotic signal, where the conventional Fourier method cannot be adopted, and calculate the time evolution of probability density functions (PDFs) and moments. Both white and colored Gaussian noises terms are included to describe fluctuations. Our calculations show that time-dependent PDFs obtained by VSGA agree excellently with those obtained by Monte Carlo simulations. The correlation between the chaotic input signal and the mean response are also calculated as a function of the noise intensity, which confirms the occurrence of aperiodic stochastic resonance with both white and colored noises.