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arXiv · 1403.1068

The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor

Thai Son Doan·Martin Rasmussen·Peter E. Kloeden
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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.

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Thai Son Doan, Martin Rasmussen, Peter E. Kloeden. 2014-03-05. The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor. https://arxiv.org/abs/1403.1068

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