Méndez V, Campos D, Horsthemke W. Stationary energy probability density of oscillators driven by a random external force.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013;
87:062132. [PMID:
23848652 DOI:
10.1103/physreve.87.062132]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2013] [Indexed: 06/02/2023]
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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