  Transient properties of different physical systems with metastable states
perturbed by external white noise have been investigated. Two noise-induced
phenomena, namely the noise enhanced stability and the resonant activation, are
theoretically predicted in a piece-wise linear fluctuating potential with a
metastable state. The enhancement of the lifetime of metastable states due to
the noise, and the suppression of noise through resonant activation phenomenon
will be reviewed in models of interdisciplinary physics: (i) dynamics of an
overdamped Josephson junction; (ii) transient regime of the noisy
FitzHugh-Nagumo model; (iii) population dynamics.
