Probabilistic analysis of random nonlinear oscillators subject to small perturbations via probability density functions: theory and computing

• Published in: European physical journal plus Vol. 136; no. 7; p. 723
• Main Authors: Cortés, Juan-Carlos, López-Navarro, Elena, Romero, José-Vicente, Roselló, María-Dolores
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2021; Springer Nature B.V
• Subjects: Applied and Technical Physics; Approximation; Atomic; Complex Systems; Condensed Matter Physics; Degrees of freedom; Focus Point on Uncertainty Quantification of Modelling and Simulation in Physics and Related Areas: From Theoretical to Computational Techniques; Gaussian process; Mathematical analysis; Mathematical and Computational Physics; Maximum entropy; Molecular; Nonlinearity; Optical and Plasma Physics; Oscillators; Perturbation methods; Physics; Physics and Astronomy; Probabilistic analysis; Probability density functions; Probability theory; Random variables; Regular Article; Statistical analysis; Steady state; Stochastic models; Stochastic processes; Theoretical
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-021-01672-w

We study a class of single-degree-of-freedom oscillators whose restoring function is affected by small nonlinearities and excited by stationary Gaussian stochastic processes. We obtain, via the stochastic perturbation technique, approximations of the main statistics of the steady state, which is a random variable, including the first moments, and the correlation and power spectral functions. Additionally, we combine this key information with the principle of maximum entropy to construct approximations of the probability density function of the steady state. We include two numerical examples where the advantages and limitations of the stochastic perturbation method are discussed with regard to certain general properties that must be preserved.