scholarly journals Discrete N-barrier maximum principle for a lattice dynamical system arising in competition models

2020 ◽  
Vol 40 (1) ◽  
pp. 153-187
Author(s):  
Chiun-Chuan Chen ◽  
◽  
Ting-Yang Hsiao ◽  
Li-Chang Hung ◽  
Keyword(s):  
Dynamical System ◽  
Maximum Principle ◽  
Competition Models ◽  
Lattice Dynamical System

Stability of Traveling Wavefronts for a Two-Component Lattice Dynamical System Arising in Competition Models

2018 ◽  
Vol 61 (2) ◽  
pp. 423-437 ◽  
Author(s):  
Guo-Bao Zhang ◽  
Ge Tian
Keyword(s):  
Dynamical System ◽  
Initial Perturbation ◽  
Asymptotically Stable ◽  
One Dimensional ◽  
Weighted Energy ◽  
Competition Models ◽  
Lattice Dynamical System ◽  
Two Component ◽  
Spatial Lattice ◽  
Large Speed

AbstractIn this paper, we study a two-component Lotka–Volterra competition systemon a one-dimensional spatial lattice. By the comparison principle, together with the weighted energy, we prove that the traveling wavefronts with large speed are exponentially asymptotically stable, when the initial perturbation around the traveling wavefronts decays exponentially as j + ct → −∞, where j ∈ , t > 0, but the initial perturbation can be arbitrarily large on other locations. This partially answers an open problem by J.-S. Guo and C.-H.Wu.

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.

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.

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