Long Term Behavior for a Class of Stochastic Delay Lattice Systems in Xρ Space

Long Term Behavior for a Class of Stochastic Delay Lattice Systems in Xρ Space

In this paper, we focus on the asymptotic behavior of solutions to stochastic delay lattice equations with additive noise and deterministic forcing. We first show the existence of a continuous random dynamical system for the equations. Then we investigate the pullback asymptotical compactness of sol...

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Main Authors: Yijin Zhang, Zongbing Lin
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2020/5405947
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spelling doaj-41399685e1b4479d9aa49bfba76cc7002020-11-25T01:27:03ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/54059475405947Long Term Behavior for a Class of Stochastic Delay Lattice Systems in Xρ SpaceYijin Zhang0Zongbing Lin1School of Mathematics, Sichuan University, Chengdu, Sichuan 610065, ChinaSchool of Mathematics and Computer Science, Panzhihua University, Panzhihua 617000, ChinaIn this paper, we focus on the asymptotic behavior of solutions to stochastic delay lattice equations with additive noise and deterministic forcing. We first show the existence of a continuous random dynamical system for the equations. Then we investigate the pullback asymptotical compactness of solutions as well as the existence and uniqueness of tempered random attractor in Xρ space. Finally, ergodicity of the systems is achieved.http://dx.doi.org/10.1155/2020/5405947
collection DOAJ
language English
format Article
sources DOAJ
author Yijin Zhang
Zongbing Lin
spellingShingle Yijin Zhang
Zongbing Lin
Long Term Behavior for a Class of Stochastic Delay Lattice Systems in Xρ Space
Discrete Dynamics in Nature and Society
author_facet Yijin Zhang
Zongbing Lin
author_sort Yijin Zhang
title Long Term Behavior for a Class of Stochastic Delay Lattice Systems in Xρ Space
title_short Long Term Behavior for a Class of Stochastic Delay Lattice Systems in Xρ Space
title_full Long Term Behavior for a Class of Stochastic Delay Lattice Systems in Xρ Space
title_fullStr Long Term Behavior for a Class of Stochastic Delay Lattice Systems in Xρ Space
title_full_unstemmed Long Term Behavior for a Class of Stochastic Delay Lattice Systems in Xρ Space
title_sort long term behavior for a class of stochastic delay lattice systems in xρ space
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2020-01-01
description In this paper, we focus on the asymptotic behavior of solutions to stochastic delay lattice equations with additive noise and deterministic forcing. We first show the existence of a continuous random dynamical system for the equations. Then we investigate the pullback asymptotical compactness of solutions as well as the existence and uniqueness of tempered random attractor in Xρ space. Finally, ergodicity of the systems is achieved.
url http://dx.doi.org/10.1155/2020/5405947
work_keys_str_mv AT yijinzhang longtermbehaviorforaclassofstochasticdelaylatticesystemsinxrspace
AT zongbinglin longtermbehaviorforaclassofstochasticdelaylatticesystemsinxrspace
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