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.

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 OF STOCHASTIC LATTICE DYNAMICAL SYSTEMS DRIVEN BY FRACTIONAL BROWNIAN MOTIONS

2013 ◽  
Vol 23 (03) ◽  
pp. 1350041 ◽  
Author(s):  
ANHUI GU
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Existence And Uniqueness ◽  
Random Attractor ◽  
Hurst Parameter ◽  
Random Dynamical System ◽  
Brownian Motions ◽  
Fractional Brownian Motions ◽  
Random Attractors ◽  
Lattice Dynamical Systems

This paper is devoted to consider stochastic lattice dynamical systems (SLDS) driven by fractional Brownian motions with Hurst parameter bigger than 1/2. Under usual dissipativity conditions these SLDS are shown to generate a random dynamical system for which the existence and uniqueness of a random attractor are established. Furthermore, the random attractor is, in fact, a singleton sets random attractor.

scholarly journals Attractors for non-autonomous retarded lattice dynamical systems

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Tomás Caraballo ◽  
Francisco Morillas ◽  
José Valero
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Nonlinear Term ◽  
Pullback Attractor ◽  
System With Delay ◽  
General Growth ◽  
Lattice Dynamical System ◽  
Lattice Dynamical Systems ◽  
Autonomous Dynamical System

AbstractIn this paperwe study a non-autonomous lattice dynamical system with delay. Under rather general growth and dissipative conditions on the nonlinear term,we define a non-autonomous dynamical system and prove the existence of a pullback attractor for such system as well. Both multivalued and single-valued cases are considered.

scholarly journals Random attractors for stochastic lattice dynamical systems with infinite multiplicative white noise

2016 ◽  
Vol 130 ◽  
pp. 255-278 ◽  
Author(s):  
Tomás Caraballo ◽  
Xiaoying Han ◽  
Björn Schmalfuss ◽  
José Valero
Keyword(s):  
Dynamical Systems ◽  
White Noise ◽  
Random Attractors ◽  
Multiplicative White Noise ◽  
Lattice Dynamical Systems

DENSITY OF MEASURE-THEORETIC DIRECTIONAL ENTROPY FOR LATTICE DYNAMICAL SYSTEMS

2008 ◽  
Vol 18 (01) ◽  
pp. 161-168 ◽  
Author(s):  
M. COURBAGE ◽  
B. KAMIŃSKI
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Constant Function ◽  
Shift Transformation ◽  
Lattice Dynamical System ◽  
Lattice Dynamical Systems

The density of the measure-theoretic directional entropy for the lattice dynamical system is introduced and it is shown that for a lattice dynamical transformation commuting with the shift transformation the density coincides with the entropy of the ℤ2-action generated by these two transformations, i.e. it is a constant function with respect to the direction. It is also proved that in the noncommutative case this result fails to be true.

scholarly journals Upper semicontinuity of the attractor for lattice dynamical systems of partly dissipative reaction diffusion systems

2005 ◽  
Vol 2005 (3) ◽  
pp. 273-288 ◽  
Author(s):  
Ahmed Y. Abdallah
Keyword(s):  
Dynamical System ◽  
Hilbert Space ◽  
Upper Semicontinuity ◽  
Reaction Diffusion ◽  
Dimensional Lattice ◽  
Reaction Diffusion Systems ◽  
Infinite Dimensional ◽  
Diffusion Systems ◽  
Lattice Dynamical System ◽  
Lattice Dynamical Systems

We investigate the existence of a global attractor and its upper semicontinuity for the infinite-dimensional lattice dynamical system of a partly dissipative reaction diffusion system in the Hilbert spacel2×l2. Such a system is similar to the discretized FitzHugh-Nagumo system in neurobiology, which is an adequate justification for its study.

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 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.

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