Convergence to local random attractors [PDF]
Dynamical Systems, 2003 Random attractors allow one to classify qualitative and quantitative aspects of the long-time behaviourof stochastically forced systems viewed as random dynamical systems (RDS) in an analogous way to attractors for deterministic systems. We compare several notions of random attractor in RDS by examining convergence of trajectories to a random invariant
Ashwin, Peter, Ochs, Gunter
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Connectedness of random set attractors [PDF]
Rendiconti Lincei, Matematica e Applicazioni, 2018 We examine the question whether random set attractors for continuous-time random dynamical systems on a connected state space are connected. In the deterministic case, these attractors are known to be connected. In the probabilistic setup, however, connectedness has only been shown under stronger connectedness assumptions on the ...
Scheutzow, Michael, Vorkastner, Isabell
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Upper semicontinuity of random attractors for non-compact random dynamical systems [PDF]
Electronic Journal of Differential Equations, 2009 The upper semicontinuity of random attractors for non-compact random dynamical systems is proved when the union of all perturbed random attractors is precompact with probability one.
Bixiang Wang
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Upper Semicontinuity of Random Attractors for Nonautonomous Stochastic Reversible Selkov System with Multiplicative Noise [PDF]
Advances in Mathematical Physics, 2019 In this paper, the existence of random attractors for nonautonomous stochastic reversible Selkov system with multiplicative noise has been proved through Ornstein-Uhlenbeck transformation.
Chunxiao Guo, Yanfeng Guo, Xiaohan Li
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Upper Semicontinuity of Attractors for a Non-Newtonian Fluid under Small Random Perturbations [PDF]
Abstract and Applied Analysis, 2014 This paper investigates the limiting behavior of attractors for a two-dimensional incompressible non-Newtonian fluid under small random perturbations. Under certain conditions, the upper semicontinuity of the attractors for diminishing perturbations is ...
Jianxin Luo
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Comment on: Criteria for Strong and Weak Random Attractors [PDF]
Journal of Dynamics and Differential EquationsAbstract In the article ’Criteria for Strong and Weak Random Attractors’ necessary and sufficient conditions for strong attractors and weak attractors are studied. In this note we correct two of its theorems on strong attractors.
Crauel, Hans +2 more
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Topological dimensions of random attractors for a stochastic reaction-diffusion equation with delay [PDF]
Electronic Journal of Qualitative Theory of Differential EquationsThe aim of this paper is to obtain an estimation of Hausdorff as well as fractal dimensions of random attractors for a stochastic reaction-diffusion equation with delay.
Wenjie Hu, Tomas Caraballo
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Periodic random attractors for stochastic Navier-Stokes equations on unbounded domains [PDF]
Electronic Journal of Differential Equations, 2012 This article concerns the asymptotic behavior of solutions to the two-dimensional Navier-Stokes equations with both non-autonomous deterministic and stochastic terms defined on unbounded domains.
Bixiang Wang
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Random periodic paths through random attractors, synchronizations and Lyapunov exponents [PDF]
, 2021 In this thesis, we discuss the existence of random periodic paths through studying random periodic attractors and synchronization of stochastic periodic semi-flows.
Yan Luo (3333027)
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Weak mean random attractors for non-local random and stochastic reaction-diffusion equations [PDF]
, 2021 In this paper, we prove the existence of weak pullback mean random attractors for a non-local stochastic reaction-diffusion equation with a nonlinear multiplicative noise.
Valero, José +2 more
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