The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor
Dynamical Systems
2014-03-06 v1
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.
Keywords
Cite
@article{arxiv.1403.1068,
title = {The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor},
author = {Thai Son Doan and Martin Rasmussen and Peter E. Kloeden},
journal= {arXiv preprint arXiv:1403.1068},
year = {2014}
}