The present paper is concerned with transient phenomena near the instability points of dynamic systems. The problem of decay of unstable states is investigated in the framework of the model of overdamped Brownian motion. It is shown that in many physical situations the additive noise can increase the decay time of unstable states, in contrast with accepted notions. The conditions for this effect are studied in detail. Physical examples are considered.

• Received 18 July 1997

DOI:https://doi.org/10.1103/PhysRevE.57.2618