Relaxation of probability characteristics of the brownian motion of a nonlinear oscillator

We consider an oscillator with nonlinear elasticity and nonlinear damping under the action of a Gaussian delta-correlated random force. The oscillator is treated as a Brownian particle in the corresponding potential profile. We analyze the problem using the analytical-numerical method based on solvi...

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Bibliographic Details
Published in:Radiophysics and quantum electronics 2000-05, Vol.43 (5), p.422-431
Main Author: Muzychuk, O V
Format: Article
Language:English
Subjects:
Damping
Differential equations
Elasticity
Evolution
Gaussian
Mathematical analysis
Nonlinearity
Oscillations
Oscillators
Probability
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Summary:We consider an oscillator with nonlinear elasticity and nonlinear damping under the action of a Gaussian delta-correlated random force. The oscillator is treated as a Brownian particle in the corresponding potential profile. We analyze the problem using the analytical-numerical method based on solving the chain of differential equations for the statistical moments, which is broken in a certain manner. For the case of nonlinear elasticity, we find the dependence of the relaxation times of the mean values and variances of both the coordinates and velocities on the system parameters and noise intensity. By analogy, the relaxation of the probability characteristics of the oscillation amplitude is studied for a system with nonlinear damping. In both cases, the evolution of the Gaussian or Rayleigh probability distributions is described on the basis of the moment relaxation.[PUBLICATION ABSTRACT]
ISSN:0033-8443
1573-9120
DOI:10.1007/BF02677160