  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.
