Open AccessThe mean-square dichotomy spectrum and a bifurcation to a mean-square attractor
Author(s) -
Thai Son Doan,
Martin Rasmussen,
Peter E. Kloeden
Publication year - 2015
Publication title -
discrete and continuous dynamical systems - b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2015.20.875
Subject(s) - mathematics , mean square , attractor , square (algebra) , spectrum (functional analysis) , bifurcation , sign (mathematics) , mean field theory , mathematical analysis , pure mathematics , physics , geometry , nonlinear system , quantum mechanics
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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