Stochastically perturbed Hopf bifurcation
type: Item
instance of: scholarly article
title: Stochastically perturbed Hopf bifurcation
zbMATH Open document ID: 0635.34037
DOI: 10.1016/0020-7462(87)90029-1
author: N. Sri Namachchivaya
author: S. T. Ariaratnam
published in: International Journal of Non-Linear Mechanics
publication date: 1987-01-01T00:00:00Z
review text: A two-dimensional system of differential equations \[ \frac{dy}{dt}=F(y,\sigma)+\epsilon^{1/2}[A_ 1(\sigma)f(t)+A_ 2(\sigma)g(t)]y \] is considered where F is a vector function analytic in y and \(\sigma\), \(\sigma\) is a real-valued parameter, \(A_ 1(\sigma)\), \(A_ 2(\sigma)\) are \(2\times 2\)-matrices which depend only on \(\sigma\), f(t), g(t) are uncorrelated stationary processes with zero mean values, \(\epsilon\) is a small parameter and \(\epsilon \ll 1\). The processes f(t), g(t) have small correlation time and smooth spectral density. The system undergoes a Hopf bifurcation at \(\sigma =\sigma_ c\). The paper studies almost sure and moment stability of the trivial and bifurcating solutions.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 4034169
zbMATH Keywords: diffusion approximation
zbMATH Keywords: spectral density
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: bifurcating solutions
MaRDI profile type: Publication
full work available at URL: 0020-7462(87)90029-1
OpenAlex ID: W1979522165
description: scientific article; zbMATH DE number 4034169