Multimodality in systems driven by Ornstein-Uhlenbeck noise.

Abstract

The presence of noise in nonlinear dynamical systems can significantly change their properties. Here, we study the properties of a noise perturbed motion in a single-well potential of |x|n (n>0) type. We explore under what conditions the action of the Ornstein-Uhlenbeck noise induces bimodality of stationary states in static, single-well, power-law potentials. In particular, we inspect the transition from unimodality (n⩽2) to bimodality (n>2). Results of numerical simulations are compared with estimates obtained from the unified colored-noise approximation. Furthermore, we explore the role of a harmonic addition to the general single-well power-law potentials showing its constructive or destructive role.