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

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 r...

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Bibliographic Details
Published in:European physical journal plus 2021-07, Vol.136 (7), p.723, Article 723
Main Authors: Cortés, Juan-Carlos, López-Navarro, Elena, Romero, José-Vicente, Roselló, María-Dolores
Format: Article
Language:English
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
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Summary: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.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/s13360-021-01672-w