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The overdamped motion of a Brownian particle in randomly switching piece-wisemetastable linear potential shows noise enhanced stability (NES): the noisestabilizes the metastable system and the system remains in this state for alonger time than in the absence of white noise. The mean first passage time(MFPT) has a maximum at a finite value of white noise intensity. The analyticalexpression of MFPT in terms of the white noise intensity, the parameters of thepotential barrier, and of the dichotomous noise is derived. The conditions forthe NES phenomenon and the parameter region where the effect can be observedare obtained. The mean first passage time behaviours as a function of the meanflipping rate of the potential for unstable and metastable initialconfigurations are also analyzed. We observe the resonant activation phenomenonfor initial metastable configuration of the potential profile.Comment: 9 pages, 5 figures. In press in "European Physical Journal B

Enhancement of stability in randomly switching potential with metastable state