On the maximal Lyapunov exponent for a real noise parametrically excited co-dimension two bifurcation system. II
type: Item
instance of: scholarly article
title: On the maximal Lyapunov exponent for a real noise parametrically excited co-dimension two bifurcation system. II
zbMATH Open document ID: 0983.37064
DOI: 10.1007/BF02460323
author: Qiu Chen
author: Dapeng Chen
author: Xianbin Liu
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 2002-04-23T00:00:00Z
review text: This paper continues Part I (see Zbl 0983.37063 above) deals with a codimension two bifurcation system driven by a small-intensity real noise process. Using an asymptotic analysis given by L. Arnold and the expression of the eigenvalue spectrum of the Fokker-Planck operator, the authors obtain both the asymptotic expansion of an invariant measure and the maximal Lyapunov exponent for the problems under consideration. Note that here only the situation in which the Lyapunov exponent \(\lambda_\varepsilon\) possesses an analytically explicit expression is investigated. Moreover in order to consider a rather general model, the real noise was assumed to be the output of a linear filter system -- a zero-mean stationary Gaussian diffusion process which satisfies a detailed balance condition. The results of the authors can be used to determine the stochastic bifurcation point with probability 1 for the relevant system.
Mathematics Subject Classification ID: 37H20
Mathematics Subject Classification ID: 37D25
Mathematics Subject Classification ID: 37A05
Mathematics Subject Classification ID: 37H15
Mathematics Subject Classification ID: 34D08
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 60H30
zbMATH DE Number: 1417800
zbMATH Keywords: codimension two bifurcations
zbMATH Keywords: real-noise
zbMATH Keywords: asymptotic analysis
zbMATH Keywords: invariant measure
zbMATH Keywords: Lyapunov exponent
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Q5332526
cites work: The researches on the stability and bifurcation of nonlinear stochastic dynamical systems.
cites work: Q4314878
cites work: Stochastic stability of nonlinear systems
cites work: Lyapunov Exponents and Stochastic Stability of Two-Dimensional Parametrically Excited Random Systems
cites work: Asymptotic Analysis of the Lyapunov Exponent and Rotation Number of the Random Oscillator and Applications
cites work: On the maximal Lyapunov exponent for a real noise parametrically excited co-dimension two bifurcation system. I
full work available at URL: https://doi.org/10.1007/bf02460323
OpenAlex ID: W2051106297
description: scientific article; zbMATH DE number 1417800