Pulse replications and spatially differentiated structure formation in one-dimensional lattice dynamical system

2006 ◽  
Vol 201 (1-2) ◽  
pp. 90-100 ◽  
Author(s):  
Akinori Awazu ◽  
Kunihiko Kaneko
Keyword(s):  
Dynamical System ◽  
Structure Formation ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Lattice Dynamical System ◽  
Spatially Differentiated

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 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.

scholarly journals Global stability of traveling wave fronts in a two-dimensional lattice dynamical system with global interaction

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Cui-Ping Cheng ◽  
Ruo-Fan An
Keyword(s):  
Dynamical System ◽  
Traveling Wave ◽  
Single Species ◽  
Wave Fronts ◽  
Dimensional Lattice ◽  
Weighted Energy Method ◽  
Traveling Wave Fronts ◽  
Weighted Energy ◽  
Lattice Dynamical System ◽  
Exponentially Stable

<p style='text-indent:20px;'>This paper is concerned with the traveling wave fronts for a lattice dynamical system with global interaction, which arises in a single species in a 2D patchy environment with infinite number of patches connected locally by diffusion and global interaction by delay. We prove that all non-critical traveling wave fronts are globally exponentially stable in time, and the critical traveling wave fronts are globally algebraically stable by the weighted energy method combined with the comparison principle and the discrete Fourier transform.</p>

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.

Sign in / Sign up

Export Citation Format

Share Document