scholarly journals Wave propagation for a two-component lattice dynamical system arising in strong competition models

2011 ◽  
Vol 250 (8) ◽  
pp. 3504-3533 ◽  
Author(s):  
Jong-Shenq Guo ◽  
Chang-Hong Wu
Keyword(s):  
Dynamical System ◽  
Wave Propagation ◽  
Competition Models ◽  
Lattice Dynamical System ◽  
Two Component ◽  
Strong Competition

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 Stability of traveling wavefronts for a 2D lattice dynamical system arising in a diffusive population model

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Haiqin Zhao
Keyword(s):  
Dynamical System ◽  
Existence And Uniqueness ◽  
Population Model ◽  
Wave Speed ◽  
Exponential Convergence ◽  
Nonlinear Anal ◽  
Lattice Dynamical System ◽  
Two Component ◽  
Exponentially Stable ◽  
The Stability

Abstract This paper is concerned with the traveling wavefronts of a 2D two-component lattice dynamical system. This problem arises in the modeling of a species with mobile and stationary subpopulations in an environment in which the habitat is two-dimensional and divided into countable niches. The existence and uniqueness of the traveling wavefronts of this system have been studied in (Zhao and Wu in Nonlinear Anal., Real World Appl. 12: 1178–1191, 2011). However, the stability of the traveling wavefronts remains unsolved. In this paper, we show that all noncritical traveling wavefronts with given direction of propagation and wave speed are exponentially stable in time. In particular, we obtain the exponential convergence rate.

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.

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