Random attractors for second-order stochastic lattice dynamical systems

2010 ◽  
Vol 72 (1) ◽  
pp. 483-494 ◽  
Author(s):  
Xiaohu Wang ◽  
Shuyong Li ◽  
Daoyi Xu
Keyword(s):  
Dynamical Systems ◽  
Second Order ◽  
Random Attractors ◽  
Lattice Dynamical Systems

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 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.

A Combined Criterion for Existence and Continuity of Random Attractors for Stochastic Lattice Dynamical Systems

2017 ◽  
Vol 27 (02) ◽  
pp. 1750019 ◽  
Author(s):  
Anhui Gu ◽  
Yangrong Li
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Random Systems ◽  
Sufficient Criterion ◽  
Abstract Result ◽  
Lattice Dynamical System ◽  
Random Attractors ◽  
Multiplicative White Noise ◽  
Lattice Dynamical Systems ◽  
Set Up

The paper is devoted to establishing a combination of sufficient criterion for the existence and upper semi-continuity of random attractors for stochastic lattice dynamical systems. By relying on a family of random systems itself, we first set up the abstract result when it is convergent, uniformly absorbing and uniformly random when asymptotically null in the phase space. Then we apply the results to the second-order lattice dynamical system driven by multiplicative white noise. It is indicated that the criterion depending on the dynamical system itself seems more applicable than the existing ones to lattice differential models.

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