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

• Published in: Radiophysics and quantum electronics Vol. 43; no. 5; pp. 422 - 431
• Main Author: Muzychuk, O V
• Format: Journal Article
• Language: English
• Published: New York Springer Nature B.V 01-05-2000
• Subjects: Damping; Differential equations; Elasticity; Evolution; Gaussian; Mathematical analysis; Nonlinearity; Oscillations; Oscillators; Probability
• ISSN: 0033-8443; 1573-9120
• DOI: 10.1007/BF02677160

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]