scholarly journals Traveling wave front for a two-component lattice dynamical system arising in competition models

2012 ◽  
Vol 252 (8) ◽  
pp. 4357-4391 ◽  
Author(s):  
Jong-Shenq Guo ◽  
Chang-Hong Wu
Keyword(s):  
Dynamical System ◽  
Wave Front ◽  
Traveling Wave ◽  
Competition Models ◽  
Traveling Wave Front ◽  
Lattice Dynamical System ◽  
Two Component

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.

Spatio-Temporal Pattern Formation in Holling–Tanner Type Model with Nonlocal Consumption of Resources

2019 ◽  
Vol 29 (01) ◽  
pp. 1930002 ◽  
Author(s):  
Swadesh Pal ◽  
Malay Banerjee ◽  
S. Ghorai
Keyword(s):  
Wave Front ◽  
Traveling Wave ◽  
Traveling Wave Solution ◽  
Nonlocal Interaction ◽  
Nonlocal Term ◽  
Generalist Predator ◽  
Nonlocal Model ◽  
Traveling Wave Front ◽  
Temporal Models ◽  
Spatio Temporal

A wide variety of spatio-temporal models are available in literature which are unable to generate stationary patterns through Turing bifurcation. Introduction of nonlocal terms to the same model can produce Turing patterns and this is true even for a single species population model. In this paper, we consider a prey–predator model of Holling–Tanner type with a generalist predator and a nonlocal interaction in the intra-specific competition term of the prey population. Nonmonotonic functional response is assumed to describe consumption rate of the prey by the predator. The Turing instability condition has been studied for the model without the nonlocal term around coexisting steady states. We also determine the Turing domain in the presence of nonlocal interaction term. The spatial-Hopf bifurcation has been studied and it plays an important role to find the pure Turing domain for the nonlocal model. Furthermore, in the presence of nonlocal interaction, the nonlocal model produces traveling wave solution. Using linear stability analysis, we have obtained the wave speed for the traveling wave front analytically. With the help of numerical simulation, we have verified that the speed of the traveling wave front for the complete nonlinear nonlocal model matches with the analytical approximation. The emergence of wave trains has also been established for higher range of nonlocal interaction.

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>

Localized Traveling Wave Front in Binary Fluid Convection

1997 ◽  
pp. 138-140
Author(s):  
Masashi Nomura ◽  
Atsushi Ogawa ◽  
Yoshifumi Harada
Keyword(s):  
Wave Front ◽  
Traveling Wave ◽  
Binary Fluid ◽  
Traveling Wave Front ◽  
Fluid Convection
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