title: Variational superposed Gaussian approximation for time-dependent solutions of Langevin equations.
abstract: 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.
authors.affiliation: Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.
authors.forename: Yoshihiko
authors.initials: Y
authors.lastname: Hasegawa
mesh_terms: D003198:Computer Simulation; D009010:Monte Carlo Method; D017711:Nonlinear Dynamics; D016011:Normal Distribution; D011336:Probability; D013269:Stochastic Processes