  Stochastic resetting and noise-enhanced stability are two phenomena which can
affect the lifetime and relaxation of nonequilibrium states. They can be
considered as measures of controlling the efficiency of the completion process
when a stochastic system has to reach a desired state. Here, we study
interaction of random (Poissonian) resetting and stochastic dynamics in
unstable potentials. Unlike noise-induced stability which increases the
relaxation time, the stochastic resetting may eliminate winding trajectories
contributing to the lifetime and accelerate the escape kinetics from unstable
states. In the paper we present a framework to analyze compromises between the
two contrasting phenomena in a noise-driven kinetics subject to random
restarts.
