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

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  • 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.
    Mathematics Subject Classification: Primary: 37H15, 37H20, 60H10; Secondary: 37H10, 60H30.

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