  We study the effects of noise-intensity fluctuations on the stationary and
dynamical properties of an overdamped Langevin model with a bistable potential
and external periodical driving force. We calculated the stationary
distributions, mean-first passage time (MFPT) and the spectral amplification
factor using a complete set expansion (CSE) technique. We found resonant
activation (RA) and stochastic resonance (SR) phenomena in the system under
investigation. Moreover, the strength of RA and SR phenomena exhibit
non-monotonic behavior and their trade-off relation as a function of the
squared variation coefficient of the noise-intensity process. The reliability
of CSE is verified with Monte Carlo simulations.
