English

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}
}