Stationary energy probability density of oscillators driven by a random external force

Vicenç Méndez, Daniel Campos, and Werner Horsthemke
Phys. Rev. E 87, 062132 – Published 24 June 2013

Abstract

We derive rigorous analytical results for the stationary energy probability density function of linear and nonlinear oscillators driven by additive Gaussian noise. Our study focuses on two cases: (i) a harmonic oscillator subjected to Gaussian colored noise with an arbitrary correlation function and (ii) nonlinear oscillators with a general potential driven by Gaussian white noise. We also derive analytical expressions for the stationary moments of the energy and investigate the partition of the mean energy between kinetic and potential energy. To illustrate our general results, we consider specifically the case of exponentially correlated noise for (i) and power-law and bistable potentials for (ii). Our theoretical results are substantiated by Langevin simulations.

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  • Received 24 April 2013

DOI:https://doi.org/10.1103/PhysRevE.87.062132

©2013 American Physical Society

Authors & Affiliations

Vicenç Méndez1, Daniel Campos1, and Werner Horsthemke2

  • 1Grup de Física Estadística, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
  • 2Department of Chemistry, Southern Methodist University, Dallas, Texas 75275-0314, USA

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Issue

Vol. 87, Iss. 6 — June 2013

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