Effects of additive noise on vibrational resonance in a bistable system
Jes\'us Casado-Pascual (1), Jos\'e Pablo Baltan\'as (2) ((1), F\'isica Te\'orica, Universidad de Sevilla, Spain, (2) Departamento de, Matem\'aticas y F\'isica Aplicadas y Ciencias de la Naturaleza, Universidad, Rey Juan Carlos, Madrid, Spain)
TL;DR
This paper investigates how additive noise influences vibrational resonance in a bistable system, providing analytical expressions and validating them through numerical simulations.
Contribution
It offers new analytical formulas for vibrational resonance observables in a bistable system under noise and bichromatic forcing, validated by numerical solutions.
Findings
Analytical expressions accurately predict vibrational resonance behavior.
Numerical simulations confirm the theoretical results.
Discussion of the validity range of the analytical approach.
Abstract
We study the overdamped motion of a particle in a bistable potential subject to the action of a bichromatic force and additive noise, within the context of the vibrational resonance phenomenon. Under appropriate conditions, we obtain analytical expressions for the relevant observables which quantifies this phenomenon. The theoretical results are compared with those obtained by the numerical solution of the stochastic differential equation which describes the dynamics of the system. The limits of validity of the theoretical approach are also discussed.
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