scholarly journals Uniqueness and stability of traveling waves for periodic monostable lattice dynamical system

2009 ◽  
Vol 246 (10) ◽  
pp. 3818-3833 ◽  
Author(s):  
Jong-Shenq Guo ◽  
Chin-Chin Wu
Keyword(s):  
Dynamical System ◽  
Traveling Waves ◽  
Lattice Dynamical System

scholarly journals Uniqueness of Traveling Waves for a Two-Dimensional Bistable Periodic Lattice Dynamical System

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Chin-Chin Wu
Keyword(s):  
Dynamical System ◽  
Traveling Waves ◽  
Periodic Lattice ◽  
Two Dimensional ◽  
Periodic Media ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Sliding Method ◽  
Lattice Dynamical System ◽  
The One

We study traveling waves for a two-dimensional lattice dynamical system with bistable nonlinearity in periodic media. The existence and the monotonicity in time of traveling waves can be derived in the same way as the one-dimensional lattice case. In this paper, we derive the uniqueness of nonzero speed traveling waves by using the comparison principle and the sliding method.

scholarly journals Traveling waves for a lattice dynamical system arising in a diffusive endemic model

Nonlinearity ◽  
2017 ◽  
Vol 30 (6) ◽  
pp. 2334-2359 ◽  
Author(s):  
Yan-Yu Chen ◽  
Jong-Shenq Guo ◽  
François Hamel
Keyword(s):  
Dynamical System ◽  
Traveling Waves ◽  
Lattice Dynamical System

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.

Pullback and Uniform Exponential Attractors for Nonautonomous Boussinesq Lattice System

2015 ◽  
Vol 25 (08) ◽  
pp. 1550100 ◽  
Author(s):  
Min Zhao ◽  
Shengfan Zhou
Keyword(s):  
Dynamical System ◽  
Boussinesq Equations ◽  
Lattice System ◽  
Time Dependent ◽  
Pullback Attractor ◽  
Exponential Attractor ◽  
Uniform Attractor ◽  
Exponential Attractors ◽  
Lattice Dynamical System ◽  
External Forces

We first prove the existence of a pullback attractor and a pullback exponential attractor for a nonautonomous lattice dynamical system of nonlinear Boussinesq equations affected by time-dependent coupled coefficients and forces. Then, we prove the existence of a uniform attractor and a uniform exponential attractor for the system driven by quasi-periodic external forces.

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