scholarly journals Fractal Dimension for the Nonautonomous Stochastic Fifth-Order Swift–Hohenberg Equation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yanfeng Guo ◽  
Chunxiao Guo ◽  
Yongping Xi
Keyword(s):  
Fractal Dimension ◽  
White Noise ◽  
Bounded Domain ◽  
Unbounded Domain ◽  
Random Attractor ◽  
Additive White Noise ◽  
Random Attractors ◽  
Fifth Order

Some dynamics behaviors for the nonautonomous stochastic fifth-order Swift–Hohenberg equation with additive white noise are considered. The existence of pullback random attractors for the nonautonomous stochastic fifth-order Swift–Hohenberg equation with some properties is mainly investigated on the bounded domain and unbounded domain, through the Ornstein–Uhlenbeck transformation and tail-term estimates. Furthermore, on the basis of some conditions, the finiteness of fractal dimension of random attractor is proved.

scholarly journals Random attractors for stochastic delay wave equations on $ \mathbb{R}^n $ with linear memory and nonlinear damping

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jingyu Wang ◽  
Yejuan Wang ◽  
Lin Yang ◽  
Tomás Caraballo
Keyword(s):  
Wave Equation ◽  
White Noise ◽  
Unbounded Domain ◽  
Existence And Uniqueness ◽  
Wave Equations ◽  
Nonlinear Damping ◽  
Random Attractor ◽  
Stochastic Delay ◽  
Additive White Noise ◽  
Random Attractors

<p style='text-indent:20px;'>A non-autonomous stochastic delay wave equation with linear memory and nonlinear damping driven by additive white noise is considered on the unbounded domain <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^n $\end{document}</tex-math></inline-formula>. We establish the existence and uniqueness of a random attractor <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{A} $\end{document}</tex-math></inline-formula> that is compact in <inline-formula><tex-math id="M3">\begin{document}$ C{([-h, 0];H^1(\mathbb{R}^n))}\times C{([-h, 0];L^2(\mathbb{R}^n))}\times L_\mu^2(\mathbb{R}^+;H^1(\mathbb{R}^n)) $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M4">\begin{document}$ 1\leqslant n \leqslant 3 $\end{document}</tex-math></inline-formula>.</p>

Dynamics of stochastic FitzHugh–Nagumo systems with additive noise on unbounded thin domains

2019 ◽  
Vol 20 (03) ◽  
pp. 2050018
Author(s):  
Lin Shi ◽  
Dingshi Li ◽  
Xiliang Li ◽  
Xiaohu Wang
Keyword(s):  
Asymptotic Behavior ◽  
White Noise ◽  
Unbounded Domain ◽  
Existence And Uniqueness ◽  
Additive Noise ◽  
Upper Semicontinuity ◽  
Thin Domains ◽  
Additive White Noise ◽  
Random Attractors ◽  
Lower Dimensional

We investigate the asymptotic behavior of a class of non-autonomous stochastic FitzHugh–Nagumo systems driven by additive white noise on unbounded thin domains. For this aim, we first show the existence and uniqueness of random attractors for the considered equations and their limit equations. Then, we establish the upper semicontinuity of these attractors when the thin domains collapse into a lower-dimensional unbounded domain.

scholarly journals Random Attractors for Stochastic Retarded Lattice Dynamical Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Xiaoquan Ding ◽  
Jifa Jiang
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
White Noise ◽  
Random Attractor ◽  
Additive White Noise ◽  
Lattice Dynamical System ◽  
Random Attractors ◽  
Lattice Dynamical Systems ◽  
Bounded Sets

This paper is devoted to a stochastic retarded lattice dynamical system with additive white noise. We extend the method of tail estimates to stochastic retarded lattice dynamical systems and prove the existence of a compact global random attractor within the set of tempered random bounded sets.

scholarly journals Random Attractors for Stochastic Three-Component Reversible Gray-Scott System on Infinite Lattices

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Anhui Gu ◽  
Zhaojuan Wang ◽  
Shengfan Zhou
Keyword(s):  
Dynamical System ◽  
White Noise ◽  
Random Attractor ◽  
Random Dynamical System ◽  
Random Attractors ◽  
Multiplicative White Noise ◽  
Infinite Lattices

We prove the existence of a compact random attractor for the random dynamical system generated by stochastic three-component reversible Gray-Scott system with a multiplicative white noise on infinite lattices.

Wong–Zakai approximations of second-order stochastic lattice systems driven by additive white noise

2021 ◽  
pp. 2150050
Author(s):  
Yiju Chen ◽  
Chunxiao Guo ◽  
Xiaohu Wang
Keyword(s):  
White Noise ◽  
Additive Noise ◽  
Upper Semicontinuity ◽  
Second Order ◽  
Pullback Attractors ◽  
Lattice Systems ◽  
Additive White Noise ◽  
Random Attractors ◽  
Approximate System

In this paper, we study the Wong–Zakai approximations of a class of second-order stochastic lattice systems with additive noise. We first prove the existence of tempered pullback attractors for lattice systems driven by an approximation of the white noise. Then, we establish the upper semicontinuity of random attractors for the approximate system as the size of approximation approaches zero.

Limiting dynamics for stochastic FitzHugh–Nagumo equations on large domains

2019 ◽  
Vol 19 (05) ◽  
pp. 1950037 ◽  
Author(s):  
Yangrong Li ◽  
Fuzhi Li
Keyword(s):  
Bounded Domain ◽  
Unbounded Domain ◽  
Bounded Domains ◽  
Limit Set ◽  
Coupled Equations ◽  
Lower Semi ◽  
The Family ◽  
Random Attractors ◽  
Nagumo Equations ◽  
Theoretical Results

This paper is devoted to the convergence of bi-spatial random attractors as a family of bounded domains is extended to be unbounded. Some criteria in terms of expansion and restriction are provided to ensure that the unbounded-domain attractor is approximated by the family of bounded-domain attractors in both upper and lower semi-continuity senses. The theoretical results are applied to show that the stochastic FitzHugh–Nagumo coupled equations have an attractor in [Formula: see text]-times Lebesgue space irrespective of whether the domain is bounded or unbounded. Furthermore, we prove that the family of bounded-domain attractors continuously converges to the unbounded-domain attractor, and the latter can be constructed by the metric-limit set of all bounded-domain attractors.

Stochastic Euler–Bernoulli beam driven by additive white noise: Global random attractors and global dynamics

2019 ◽  
Vol 185 ◽  
pp. 216-246 ◽  
Author(s):  
Huatao Chen ◽  
Juan Luis García Guirao ◽  
Dengqing Cao ◽  
Jingfei Jiang ◽  
Xiaoming Fan
Keyword(s):  
White Noise ◽  
Global Dynamics ◽  
Bernoulli Beam ◽  
Additive White Noise ◽  
Random Attractors ◽  
Euler Bernoulli Beam
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