Traveling wave solutions for a predator–prey system with two predators and one prey

2020 ◽  
Vol 54 ◽  
pp. 103111
Author(s):  
Jong-Shenq Guo ◽  
Ken-Ichi Nakamura ◽  
Toshiko Ogiwara ◽  
Chin-Chin Wu
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Predator Prey ◽  
Wave Solutions ◽  
Prey System

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.

TRAVELING WAVES IN A REACTION-DIFFUSION PREDATOR-PREY SYSTEM WITH NONLOCAL DELAYS

2012 ◽  
Vol 05 (05) ◽  
pp. 1250043
Author(s):  
ZHE LI ◽  
RUI XU
Keyword(s):  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Iteration Scheme ◽  
Monotonicity Condition ◽  
Predator Prey ◽  
Wave Solutions ◽  
Prey System ◽  
Theoretical Results

This paper is concerned with the existence of traveling wave solutions in a reaction-diffusion predator-prey system with nonlocal delays. By introducing a partially exponential quasi-monotonicity condition and a new cross iteration scheme, we reduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. By constructing a desirable pair of upper-lower solutions, we establish the existence of traveling wave solutions. Finally, some numerical examples are carried out to illustrate the theoretical results.

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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