The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor
File(s)
Accepted version
Author(s)
Doan, TS
Rasmussen, M
Kloeden, PE
Type
Journal Article
Abstract
The dichotomy spectrum is introduced for linear mean-square random dynamical systems, and it is shown that for finite-dimensional mean-field stochastic differential equations, the dichotomy spectrum consists of finitely many compact intervals. It is then demonstrated that a change in the sign of the dichotomy spectrum is associated with a bifurcation from a trivial to a non-trivial mean-square random attractor.
Date Issued
2015-01-01
Date Acceptance
2014-04-01
Citation
Discrete and Continuous Dynamical Systems - Series B, 2015, 20 (3), pp.875-887
ISSN
1531-3492
Publisher
American Institute of Mathematical Sciences (AIMS)
Start Page
875
End Page
887
Journal / Book Title
Discrete and Continuous Dynamical Systems - Series B
Volume
20
Issue
3
Copyright Statement
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems - Series B following peer review. The definitive publisher-authenticated version Thai Son Doan and Martin Rasmussen 2015 "THE MEAN-SQUARE DICHOTOMY SPECTRUM AND A BIFURCATION TO A MEAN-SQUARE ATTRACTOR" DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS SERIES B
Volume 20, Number 3, pp. 875–887
is available online at: https://dx.doi.org/10.3934/dcdsb.2015.20.875
Volume 20, Number 3, pp. 875–887
is available online at: https://dx.doi.org/10.3934/dcdsb.2015.20.875
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Dichotomy spectrum
mean-square random dynamical system
mean-square random attractor
bifurcation
DYNAMICAL-SYSTEMS
Publication Status
Published