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

DOI10.3934/dcdsb.2015.20.875zbMath1366.37122arXiv1403.1068OpenAlexW2028859398MaRDI QIDQ256805

Thai Son Doan, Martin Rasmussen, Peter E. Kloeden

Publication date: 10 March 2016

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.1068

zbMATH Keywords

bifurcationdichotomy spectrummean-square random attractormean-square random dynamical system

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Applications of stochastic analysis (to PDEs, etc.) (60H30) Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Generation, random and stochastic difference and differential equations (37H10) Bifurcation theory for random and stochastic dynamical systems (37H20)

Related Items (8)

Asymptotic behavior of stochastic lattice systems with a Caputo fractional time derivative ⋮ Hopf bifurcation with additive noise ⋮ Gauss-Quadrature Method for One-Dimensional Mean-Field SDEs ⋮ Robustness of nonuniform mean-square exponential dichotomies ⋮ Nonautonomous and random attractors ⋮ Nonuniform mean-square exponential dichotomies and mean-square exponential stability ⋮ Asymptotic separation between solutions of Caputo fractional stochastic differential equations ⋮ Compactness in Lebesgue–Bochner spaces of random variables and the existence of mean-square random attractors

Cites Work

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• Dynamical spectrum in random dynamical systems
• Uniform exponential dichotomy of stochastic cocycles
• Stochastic Differential Equations with Nonlocal Sample Dependence
• DICHOTOMY SPECTRUM OF NONAUTONOMOUS LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS

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