scholarly journals Pullback attractors for bi-spatial continuous random dynamical systems and application to stochastic fractional power dissipative equation on an unbounded domain

2019 ◽  
Vol 24 (7) ◽  
pp. 3395-3438
Author(s):  
Wenqiang Zhao ◽  
Keyword(s):  
Dynamical Systems ◽  
Unbounded Domain ◽  
Fractional Power ◽  
Random Dynamical Systems ◽  
Pullback Attractors ◽  
Dissipative Equation

scholarly journals Asymptotic Dynamics of Young Differential Equations

2021 ◽  
Author(s):  
Luu Hoang Duc ◽  
Phan Thanh Hong
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Random Dynamical Systems ◽  
Analytic Approach ◽  
Pullback Attractors ◽  
Random Attractors ◽  
Asymptotic Dynamics

AbstractWe provide a unified analytic approach to study the asymptotic dynamics of Young differential equations, using the framework of random dynamical systems and random attractors. Our method helps to generalize recent results (Duc et al. in J Differ Equ 264:1119–1145, 2018, SIAM J Control Optim 57(4):3046–3071, 2019; Garrido-Atienza et al. in Int J Bifurc Chaos 20(9):2761–2782, 2010) on the existence of the global pullback attractors for the generated random dynamical systems. We also prove sufficient conditions for the attractor to be a singleton, thus the pathwise convergence is in both pullback and forward senses.

scholarly journals Non-autonomous invariant sets and attractors: Random dynamical system

2020 ◽  
Vol 25 (4) ◽  
pp. 17-23
Author(s):  
Mohamedsh Imran ◽  
Ihsan Jabbar Kadhim
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Global Attractors ◽  
Random Dynamical Systems ◽  
Invariant Sets ◽  
Random Dynamical System ◽  
Pullback Attractor ◽  
Pullback Attractors ◽  
Deterministic Dynamical System

 In this paper the concepts of pullback attractor ,pullback absorbing family in (deterministic) dynamical system are defined in (random) dynamical systems. Also some main result such as (existence) of pullback attractors ,upper semi-continuous of pullback attractors and uniform and global attractors are proved in random dynamical system .

Pullback attractors for multi-valued non-compact random dynamical systems generated by semi-linear degenerate parabolic equations with unbounded delays

2016 ◽  
Vol 16 (05) ◽  
pp. 1750001 ◽  
Author(s):  
Jingyu Wang ◽  
Yejuan Wang ◽  
Dun Zhao
Keyword(s):  
Dynamical Systems ◽  
Parabolic Equations ◽  
Random Dynamical Systems ◽  
Degenerate Parabolic Equations ◽  
Pullback Attractors ◽  
Asymptotic Compactness ◽  
Unbounded Delay ◽  
Bounded Set ◽  
Degenerate Parabolic ◽  
Linear Degenerate

The theory of pullback attractors for multi-valued non-compact random dynamical systems and a method of asymptotic compactness based on the concepts of the Kuratowski measure of the non-compactness of a bounded set are used to prove the existence of pullback attractors for the multi-valued non-compact random dynamical systems associated with the semi-linear degenerate parabolic unbounded delay equations with both deterministic and random external terms.

VARIATIONAL PRINCIPLE FOR SUBADDITIVE SEQUENCE OF POTENTIALS IN BUNDLE RANDOM DYNAMICAL SYSTEMS

2009 ◽  
Vol 09 (02) ◽  
pp. 205-215 ◽  
Author(s):  
XIANFENG MA ◽  
ERCAI CHEN
Keyword(s):  
Dynamical Systems ◽  
Variational Principle ◽  
Multifractal Analysis ◽  
Weak Condition ◽  
Random Dynamical Systems ◽  
Topological Pressure ◽  
Set Up

The topological pressure is defined for subadditive sequence of potentials in bundle random dynamical systems. A variational principle for the topological pressure is set up in a very weak condition. The result may have some applications in the study of multifractal analysis for random version of nonconformal dynamical systems.

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