Results 61 to 70 of about 5,047,376 (392)
Random Attractor Associated with the Quasi-Geostrophic Equation [PDF]
Journal of Dynamics and Differential Equations, 2016 We study the long time behavior of the solutions to the 2D stochastic quasi-geostrophic equation on $\mathbb{T}^2$ driven by additive noise and real linear multiplicative noise in the subcritical case (i.e. $ >1/2$) by proving the existence of a random attractor.
Zhu, Rongchan, Zhu, Xiangchan
openaire +3 more sources
Invariant measures and random attractors of stochastic delay differential equations in Hilbert space
Electronic Journal of Qualitative Theory of Differential Equations, 2022 This paper is devoted to a general stochastic delay differential equation with infinite-dimensional diffusions in a Hilbert space. We not only investigate the existence of invariant measures with either Wiener process or Lévy jump process, but also ...
Shangzhi Li, Shangjiang Guo
doaj +1 more source
The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor [PDF]
, 2014 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
Doan, Thai Son +2 more
core +1 more source
Finite-Dimensionality of Tempered Random Uniform Attractors [PDF]
Journal of Nonlinear Science, 2021 AbstractFinite-dimensional attractors play an important role in finite-dimensional reduction of PDEs in mathematical modelization and numerical simulations. For non-autonomous random dynamical systems, Cui and Langa (J Differ Equ, 263:1225–1268, 2017) developed a random uniform attractor as a minimal compact random set which provides a certain ...
Hongyong Cui +2 more
openaire +2 more sources
Dynamical behaviors of stochastic local Swift-Hohenberg equation on unbounded domain
Journal of Inequalities and Applications, 2016 In this paper, we first study the deterministic Swift-Hohenberg equation on a bounded domain. After obtaining some a priori estimates by the uniform Gronwall inequality, we prove the existence of an attractor by the Sobolev compact embeddings.
CX Guo, YY Chen, YF Guo
doaj +1 more source
The random case of Conley's theorem
, 2005 The well-known Conley's theorem states that the complement of chain recurrent set equals the union of all connecting orbits of the flow $\phi$ on the compact metric space $X$, i.e.
Arnold L +12 more
core +3 more sources
Random Attractor of Reaction-Diffusion Hopfield Neural Networks Driven by Wiener Processes
, 2018 This paper studies the global existence and uniqueness of the mild solution for reaction-diffusion Hopfield neural networks (RDHNNs) driven by Wiener processes by applying a Schauder fixed point theorem and a priori estimate; then the random attractor ...
Xiao Liang, Linshan Wang, Ruili Wang
semanticscholar +1 more source
Random attractor for stochastic non-autonomous damped wave equation with critical exponent
, 2016 In this paper, we prove the existence of random attractor and obtainan upper bound of fractal dimension of random attractor forstochastic non-autonomous damped wave equation with criticalexponent and additive white noise.
Zhaojuan Wang, Shengfan Zhou
semanticscholar +1 more source
Random Attractors for Stochastic Retarded Reaction-Diffusion Equations on Unbounded Domains
Abstract and Applied Analysis, 2013 This paper is devoted to a stochastic retarded reaction-diffusion equation on all d-dimensional space with additive white noise. We first show that the stochastic retarded reaction-diffusion equation generates a random dynamical system by transforming ...
Xiaoquan Ding, Jifa Jiang
doaj +1 more source