Multimodal stationary states in symmetric single-well potentials driven by Cauchy noise

Abstract

Stationary states for a particle moving in a single-well, steeper than parabolic, potential driven by L\'evy noise can be bi-modal. Here, we explore in details conditions that are required in order to induce multimodal stationary states having more than two modal values. Phenomenological arguments determining necessary conditions for emergence of stationary states of higher multimodality are provided. Basing on these arguments, appropriate symmetric single-well potentials are constructed. Finally, using numerical methods it is verified that stationary states have anticipated multimodality.