Noise perturbations of a nonlinear system with multiple steady states
type: Item
instance of: scholarly article
title: Noise perturbations of a nonlinear system with multiple steady states
zbMATH Open document ID: 0824.70016
DOI: 10.1016/0020-7462(94)90069-8
author: R. Valéry Roy
published in: International Journal of Non-Linear Mechanics
publication date: 1995-11-15T00:00:00Z
review text: This paper concerns a Duffing oscillator governed by the stochastic differential equation \(x''(t)+ 2\eta \omega_ 0 x'(t)+ \gamma \omega_ 0^ 2 x^ 3 (t)= \Gamma\cos \Omega t+ \zeta(t)\), where \(\zeta(t)\) is a small, white Gaussian noise. Attractors yielding two stable oscillatory states are identified, and the steady state probability density function of the fluctuations about these stable states is approximated. The time spent in a given stable state is examined by approximating the mean first passage time from its domain of attraction to that of the other state. Simulation results are presented that agree well with results obtained by using these approximations.
Mathematics Subject Classification ID: 70L05
Mathematics Subject Classification ID: 70K40
zbMATH DE Number: 707513
zbMATH Keywords: Duffing oscillator
zbMATH Keywords: stochastic differential equation
zbMATH Keywords: white Gaussian noise
zbMATH Keywords: steady state probability density function
zbMATH Keywords: mean first passage time
zbMATH Keywords: domain of attraction
reviewed by: Melvin D. Lax
MaRDI profile type: Publication
full work available at URL: 0020-7462(94)90069-8
OpenAlex ID: W2136136039
description: scientific article; zbMATH DE number 707513