Transient multimodality in relaxation from an unstable state

We analyze a relaxation process from an unstable state during which transient multimodality occurs. This phenomenon is investigated experimentally on an electronic analog circuit which mimics an overdamped bistable oscillator driven by Gaussian white noise. The oscillator potential is a sixth-order polynomial U(x). The measured times and positions at which new maxima appear in the probability distribution function agree well with the theoretical predictions. Although the initial stage of relaxation is governed by the noise the occurrence of transient multimodality is of the deterministic nature only. It is shown that the shape of the potential allows for the coexistence of three probability distribution peaks during a sizable interval of time, even though there is no long ‘‘flat’’ region in the potential where U’(x) is very small. Finally, the concept of marginality with reference to unsteady states is discussed.