Bimodality and hysteresis in systems driven by confined L\'evy flights

TL;DR

This paper studies how asymmetric Le9vy noise influences the behavior of an overdamped quartic oscillator, revealing bimodality and hysteresis effects driven by noise asymmetry.

Contribution

It demonstrates the emergence of bimodality and hysteresis in a stochastic system under asymmetric Le9vy noise, highlighting the impact of noise asymmetry on stationary states.

Findings

Bimodality appears in the stationary probability density profiles.

Hysteresis occurs when varying the noise asymmetry cyclically.

Stationary state stability depends on noise asymmetry parameter.

Abstract

We demonstrate occurrence of bimodality and dynamical hysteresis in a system describing an overdamped quartic oscillator perturbed by additive white and asymmetric L\'evy noise. Investigated estimators of the stationary probability density profiles display not only a turnover from unimodal to bimodal character but also a change in a relative stability of stationary states that depends on the asymmetry parameter of the underlying noise term. When varying the asymmetry parameter cyclically, the system exhibits a hysteresis in the occupation of a chosen stationary state.