scholarly journals Upper Semicontinuity of Random Attractors for Nonautonomous Stochastic Reversible Selkov System with Multiplicative Noise

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Chunxiao Guo ◽  
Yanfeng Guo ◽  
Xiaohan Li
Keyword(s):  
Multiplicative Noise ◽  
Upper Semicontinuity ◽  
Random Attractor ◽  
Main Difficulty ◽  
Asymptotic Compactness ◽  
Random Attractors

In this paper, the existence of random attractors for nonautonomous stochastic reversible Selkov system with multiplicative noise has been proved through Ornstein-Uhlenbeck transformation. Furthermore, the upper semicontinuity of random attractors is discussed when the intensity of noise approaches zero. The main difficulty is to prove the asymptotic compactness for establishing the existence of tempered pullback random attractor.

scholarly journals Asymptotic behavior of non-autonomous fractional stochastic lattice systems with multiplicative noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yiju Chen ◽  
Xiaohu Wang
Keyword(s):  
Asymptotic Behavior ◽  
Multiplicative Noise ◽  
Upper Semicontinuity ◽  
Random Attractor ◽  
Discrete Laplacian ◽  
Lattice Systems ◽  
Random Attractors ◽  
Infinite Range Interactions ◽  
Infinite Range

<p style='text-indent:20px;'>In this paper, we study the asymptotic behavior of non-autonomous fractional stochastic lattice systems with multiplicative noise. The considered systems are driven by the fractional discrete Laplacian, which features the infinite-range interactions. We first prove the existence of pullback random attractor in <inline-formula><tex-math id="M1">\begin{document}$ \ell^2 $\end{document}</tex-math></inline-formula> for stochastic lattice systems. The upper semicontinuity of random attractors is also established when the intensity of noise approaches zero.</p>

scholarly journals Existence of Random Attractors for a Class of Second-Order Lattice Dynamical Systems with Brownian Motions

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Yamin Wang ◽  
Ziqiao Huang ◽  
Fuad E. Alsaadi ◽  
Stanislao Lauria ◽  
Yurong Liu
Keyword(s):  
Dynamical Systems ◽  
Second Order ◽  
Random Attractor ◽  
Random Dynamical Systems ◽  
Brownian Motions ◽  
Asymptotic Compactness ◽  
Random Attractors ◽  
Lattice Dynamical Systems ◽  
Uniqueness And Existence ◽  
Special Case

This paper is concerned with the random attractors for a class of second-order stochastic lattice dynamical systems. We first prove the uniqueness and existence of the solutions of second-order stochastic lattice dynamical systems in the spaceF=lλ2×l2. Then, by proving the asymptotic compactness of the random dynamical systems, we establish the existence of the global random attractor. The system under consideration is quite general, and many existing results can be regarded as the special case of our results.

scholarly journals Random Attractors for Stochastic Retarded 2D-Navier-Stokes Equations with Additive Noise

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Xiaoyao Jia ◽  
Xiaoquan Ding
Keyword(s):  
Additive Noise ◽  
Stochastic Equation ◽  
Stokes Equations ◽  
Upper Semicontinuity ◽  
Random Attractor ◽  
Navier Stokes ◽  
Pullback Attractor ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Random Attractors

In this paper, the existence and the upper semicontinuity of a pullback attractor for stochastic retarded 2D-Navier-Stokes equation on a bounded domain are obtained. We first transform the stochastic equation into a random equation and then obtain the existence of a random attractor for random equation. Then conjugation relation between two random dynamical systems implies the existence of a random attractor for the stochastic equation. At last, we get the upper semicontinuity of random attractor.

scholarly journals Random Attractors of Stochastic Three-Component Reversible Gray-Scott System on Unbounded Domains

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Anhui Gu
Keyword(s):  
Dynamical System ◽  
A Priori Estimates ◽  
A Priori ◽  
Unbounded Domains ◽  
Random Attractor ◽  
Random Dynamical System ◽  
Far Field ◽  
Asymptotic Compactness ◽  
Priori Estimates ◽  
Random Attractors

The existence of a pullback random attractor is established for a stochastic three-component reversible Gray-Scott system on unbounded domains. The Gray-Scott system is recast as a random dynamical system and asymptotic compactness which is illustrated by using uniform, a priori estimates for far-field values of solutions and a cutoff technique.

Dynamic behavior of stochastic p-Laplacian-type lattice equations

2016 ◽  
Vol 17 (05) ◽  
pp. 1750040 ◽  
Author(s):  
Anhui Gu ◽  
Yangrong Li
Keyword(s):  
Dynamic Behavior ◽  
Multiplicative Noise ◽  
Finite Lattice ◽  
Unbounded Domains ◽  
Random Attractor ◽  
Infinite Lattice ◽  
Lower Semi ◽  
The Family ◽  
Random Attractors ◽  
Type Lattice

In this paper, we consider the dynamic behavior of stochastic [Formula: see text]-Laplacian-type lattice equations perturbed by a multiplicative noise. Under weaker dissipative conditions compared to the cases of stochastic [Formula: see text]-Laplacian-type equations in bounded and unbounded domains, we first obtain the existence of a unique random attractor. We also establish the approximation of the random attractors from finite lattice to infinite lattice, which indicates that the family of random attractors is upper and lower semi-continuous when the number of the lattice nodes tends to infinity.

scholarly journals Random Attractors for the Stochastic Discrete Long Wave-Short Wave Resonance Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Jie Xin ◽  
Hong Lu
Keyword(s):  
Dynamical System ◽  
Short Wave ◽  
Random Attractor ◽  
Random Dynamical System ◽  
Asymptotic Compactness ◽  
Infinite Lattice ◽  
Long Wave ◽  
Wave Resonance ◽  
Random Attractors

We prove the existence of the random attractor for the stochastic discrete long wave-short wave resonance equations in an infinite lattice. We prove the asymptotic compactness of the random dynamical system and obtain the random attractor.

scholarly journals Random attractors for semilinear reaction-diffusion equation with distribution derivatives and multiplicative noise on \(\mathbb{R}^{n}\)

2020 ◽  
Vol 4 (1) ◽  
pp. 126-141
Author(s):  
Fadlallah Mustafa Mosa ◽  
◽  
Abdelmajid Ali Dafallah ◽  
Eshag Mohamed Ahmed ◽  
Mohamed Y. A Bakhet ◽  
...  
Keyword(s):  
Diffusion Equation ◽  
Multiplicative Noise ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Random Attractors
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