# Noise-induced transitions in a double-well excitable oscillator

## TL;DR

This paper investigates how noise influences a double-well oscillator with nonlinear dissipation, revealing noise-induced transitions and coherence resonance through numerical and circuit simulations.

## Contribution

It introduces a detailed analysis of noise effects on a double-well oscillator, highlighting the conditions for coherence resonance and the qualitative changes in stochastic dynamics.

## Key findings

- Coexistence of two stable limit cycles in the self-sustained regime.
- Noise can induce coherence resonance in the excitable regime.
- Probability density functions change qualitatively with noise intensity.

## Abstract

The model of a double-well oscillator with nonlinear dissipation is studied. The self-sustained oscillations regime and the excitable one are described. The first regime consists in the coexistence of two stable limit cycles in the phase space, which correspond to the self-sustained oscillations of the point mass in either potential well. The self-sustained oscillations do not occur in a noise-free system in the excitable regime, but appropriate conditions for coherence resonance in either potential well can be achieved. The stochastic dynamics in both two regimes is researched by using numerical simulation and electronic circuit implementation of the considered system. Multiple qualitative changes of the probability density function (PDF) caused by noise intensity varying are explained by using the phase space structure of the deterministic system.