A General Approach to the Asymptotic Behavior of Traveling Waves in a Class of Three-Component Lattice Dynamical Systems

2016 ◽  
Vol 28 (2) ◽  
pp. 317-338 ◽  
Author(s):  
Chang-Hong Wu
Keyword(s):  
Asymptotic Behavior ◽  
Dynamical Systems ◽  
Traveling Waves ◽  
Lattice Dynamical Systems

scholarly journals Traveling Waves in Lattice Dynamical Systems

1998 ◽  
Vol 149 (2) ◽  
pp. 248-291 ◽  
Author(s):  
Shui-Nee Chow ◽  
John Mallet-Paret ◽  
Wenxian Shen
Keyword(s):  
Dynamical Systems ◽  
Traveling Waves ◽  
Lattice Dynamical Systems

scholarly journals Existence of Traveling Waves in Lattice Dynamical Systems

2016 ◽  
Vol 04 (07) ◽  
pp. 1231-1236
Author(s):  
Xiaojun Li ◽  
Yong Jiang ◽  
Ziming Du
Keyword(s):  
Dynamical Systems ◽  
Traveling Waves ◽  
Lattice Dynamical Systems

ATTRACTORS FOR LATTICE DYNAMICAL SYSTEMS

2001 ◽  
Vol 11 (01) ◽  
pp. 143-153 ◽  
Author(s):  
PETER W. BATES ◽  
KENING LU ◽  
BIXIANG WANG
Keyword(s):  
Asymptotic Behavior ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Global Attractor ◽  
Upper Semicontinuity ◽  
Global Attractors ◽  
Asymptotic Behavior Of Solutions ◽  
Lattice Differential Equations ◽  
Finite Dimensional ◽  
Lattice Dynamical Systems

We study the asymptotic behavior of solutions for lattice dynamical systems. We first prove asymptotic compactness and then establish the existence of global attractors. The upper semicontinuity of the global attractor is also obtained when the lattice differential equations are approached by finite-dimensional systems.

scholarly journals Asymptotic behavior for second order lattice dynamical systems

2001 ◽  
Vol 6 (2) ◽  
pp. 137-143
Author(s):  
Shengfan Zhou
Keyword(s):  
Asymptotic Behavior ◽  
Dynamical Systems ◽  
Global Attractor ◽  
Second Order ◽  
Lattice Dynamical Systems

We consider the existence of the global attractor for a second order lattice dynamical systems.

Attractors for multi-valued lattice dynamical systems with nonlinear diffusion terms

2021 ◽  
Author(s):  
Panpan Zhang ◽  
Anhui Gu
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Diffusion ◽  
Upper Semicontinuity ◽  
Growth Conditions ◽  
Pullback Attractor ◽  
Random Lattice ◽  
Lipschitz Continuous ◽  
Lattice Dynamical Systems ◽  
Long Term Behavior

This paper is devoted to the long-term behavior of nonautonomous random lattice dynamical systems with nonlinear diffusion terms. The nonlinear drift and diffusion terms are not expected to be Lipschitz continuous but satisfy the continuity and growth conditions. We first prove the existence of solutions, and establish the existence of a multi-valued nonautonomous cocycle. We then show the existence and uniqueness of pullback attractors parameterized by sample parameters. Finally, we establish the measurability of this pullback attractor by the method based on the weak upper semicontinuity of the solutions.

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