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Invariant manifolds for stochastic partial differential equations
Jinqiao Duan, Kening Lu, Bjoern Schmalfuss
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite…
Generalization of the Second Bogolyubov's Theorem for Non-Almost Periodic Systems
David N. Cheban, Jinqiao Duan, Anatoly Gherco
The article is devoted to the generalization of the second Bogolyubov's theorem to non-almost periodic dynamical systems. We prove the analog of the second Bogolyubov's theorem for…
Stochastic Dynamics of a Coupled Atmosphere--Ocean Model
J. Duan, H. Gao, B. Schmalfuss
The investigation of the coupled atmosphere-ocean system is not only scientifically challenging but also practically important. We consider a coupled atmosphere-ocean model, which…
Dynamics of a Coupled Atmosphere-Ocean Model
Hongjun Gao, Jinqiao Duan
We consider a coupled atmosphere-ocean model, which involves hydrodynamics, thermodynamics and nonautonomous interaction at the air-sea interface. First, we show that the coupled a…
A Markov jump process approximation of the stochastic Burgers equation
Christoph Gugg, Jinqiao Duan
We consider the stochastic Burgers equation $ \dnachd{t} ψ(t,r) = Δψ(t,r) + \nabla ψ^2(t,r)+\sqrt{γψ(t,r)} η(t,r) $ with periodic boundary conditions, where $r \in [0,1]…
Ergodic Dynamics of the Stochastic Swift-Hohenberg System
Wei Wang, Jianhua Sun, Jinqiao Duan
The Swift-Hohenberg fluid convection system with both local and nonlocal nonlinearities under the influence of white noise is studied. The objective is to understand the difference…