Hasegawa Yoshihiko
Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Apr;91(4):042912. doi: 10.1103/PhysRevE.91.042912. Epub 2015 Apr 21.
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.
我们提出了一种变分叠加高斯近似（VSGA），用于求解受外加信号作用的朗之万方程的动力学解，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应用于由混沌信号驱动的系统，在这种情况下无法采用传统的傅里叶方法，并计算概率密度函数（PDF）和矩的时间演化。同时包含白高斯噪声项和有色高斯噪声项来描述涨落。我们的计算表明，通过VSGA获得的时间相关PDF与通过蒙特卡罗模拟获得的结果非常吻合。还计算了混沌输入信号与平均响应之间的相关性作为噪声强度的函数，这证实了白噪声和有色噪声情况下非周期随机共振的发生。
