Noise-induced transitions in a double-well oscillator with nonlinear dissipation

TL;DR

This paper investigates how additive noise influences a bistable oscillator with nonlinear dissipation, revealing multiple bifurcations in its steady-state probability density function through simulations and electronic circuit experiments.

Contribution

It introduces a model of a nonlinear dissipative bistable oscillator and characterizes its noise-induced bifurcations using numerical and experimental methods.

Findings

The system exhibits two pitchfork bifurcations in the PDF with increasing noise.

Nullclines partition phase space, explaining stochastic bifurcations.

Effective potential describes the bifurcation structure.

Abstract

We develop a model of bistable oscillator with nonlinear dissipation. Using a numerical simulation and an electronic circuit realization of this system we study its response to additive noise excitations. We show that depending on noise intensity the system undergoes multiple qualitative changes in the structure of its steady-state probability density function (PDF). In particular, the PDF exhibits two pitchfork bifurcations versus noise intensity, which we describe using an effective potential and corresponding normal form of the bifurcation. These stochastic effects are explained by the partition of the phase space by the nullclines of the deterministic oscillator.