Asymptotic Dynamics of Stochastic Lattice Differential Equations: A Review

2015 ◽  
pp. 121-136 ◽  
Author(s):  
Xiaoying Han
Keyword(s):  
Differential Equations ◽  
Lattice Differential Equations ◽  
Asymptotic Dynamics

scholarly journals Time-asymptotic Dynamics of Hermitian Riccati Differential Equations

2020 ◽  
Vol 24 (1) ◽  
pp. 131-158
Author(s):  
Yueh-Cheng Kuo ◽  
Huey-Er Lin ◽  
Shih-Feng Shieh
Keyword(s):  
Differential Equations ◽  
Riccati Differential Equations ◽  
Asymptotic Dynamics

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.

Lattice Differential Equations

2013 ◽  
Vol 10 (3) ◽  
pp. 2631-2689
Author(s):  
Guillaume James ◽  
Dmitry Pelinovsky ◽  
Zoi Rapti ◽  
Guido Schneider
Keyword(s):  
Differential Equations ◽  
Lattice Differential Equations
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