scholarly journals Traveling wave solutions for diffusive predator–prey type systems with nonlinear density dependence

2017 ◽  
Vol 74 (10) ◽  
pp. 2221-2230 ◽  
Author(s):  
Huiru Li ◽  
Haibin Xiao
Keyword(s):  
Density Dependence ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Type Systems ◽  
Prey Type ◽  
Predator Prey ◽  
Wave Solutions

scholarly journals Existence of traveling wave solutions for diffusive predator–prey type systems

2012 ◽  
Vol 252 (4) ◽  
pp. 3040-3075 ◽  
Author(s):  
Cheng-Hsiung Hsu ◽  
Chi-Ru Yang ◽  
Ting-Hui Yang ◽  
Tzi-Sheng Yang
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Type Systems ◽  
Prey Type ◽  
Predator Prey ◽  
Wave Solutions

scholarly journals Minimal Wave Speed in an Integrodifference System of Predator-Prey Type

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Baoju Sun ◽  
Fuzhen Wu
Keyword(s):  
Traveling Wave ◽  
Wave Speed ◽  
Upper And Lower Solutions ◽  
Traveling Wave Solutions ◽  
Prey Type ◽  
Predator Prey ◽  
Wave Speeds ◽  
Wave Solutions ◽  
Minimal Wave Speed ◽  
Asymptotic Spreading

This article studies the minimal wave speed of traveling wave solutions in an integrodifference predator-prey system that does not have the comparison principle. By constructing generalized upper and lower solutions and utilizing the theory of asymptotic spreading, we show the minimal wave speed of traveling wave solutions modeling the invasion process of two species by presenting the existence and nonexistence of nonconstant traveling wave solutions with any wave speeds.

scholarly journals Minimal Wave Speed in a Predator-Prey System with Distributed Time Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Fuzhen Wu ◽  
Dongfeng Li
Keyword(s):  
Time Delay ◽  
Traveling Wave ◽  
Wave Speed ◽  
Upper And Lower Solutions ◽  
Traveling Wave Solutions ◽  
Predator Prey ◽  
Wave Solutions ◽  
Prey System ◽  
Minimal Wave Speed ◽  
Distributed Time Delay

This paper is concerned with the minimal wave speed of traveling wave solutions in a predator-prey system with distributed time delay, which does not satisfy comparison principle due to delayed intraspecific terms. By constructing upper and lower solutions, we obtain the existence of traveling wave solutions when the wave speed is the minimal wave speed. Our results complete the known conclusions and show the precisely asymptotic behavior of traveling wave solutions.

Numerical Study of Periodic Traveling Wave Solutions for the Predator–Prey Model with Landscape Features

2015 ◽  
Vol 25 (09) ◽  
pp. 1550117 ◽  
Author(s):  
Ana Yun ◽  
Jaemin Shin ◽  
Yibao Li ◽  
Seunggyu Lee ◽  
Junseok Kim
Keyword(s):  
Boundary Condition ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Dirichlet Boundary ◽  
Numerical Technique ◽  
Traveling Wave Solutions ◽  
Predator Prey ◽  
Landscape Features ◽  
Wave Solutions ◽  
Periodic Traveling Wave

We numerically investigate periodic traveling wave solutions for a diffusive predator–prey system with landscape features. The landscape features are modeled through the homogeneous Dirichlet boundary condition which is imposed at the edge of the obstacle domain. To effectively treat the Dirichlet boundary condition, we employ a robust and accurate numerical technique by using a boundary control function. We also propose a robust algorithm for calculating the numerical periodicity of the traveling wave solution. In numerical experiments, we show that periodic traveling waves which move out and away from the obstacle are effectively generated. We explain the formation of the traveling waves by comparing the wavelengths. The spatial asynchrony has been shown in quantitative detail for various obstacles. Furthermore, we apply our numerical technique to the complicated real landscape features.

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