Traveling wave solutions for Gause type predator–prey systems with density dependence: A heteroclinic orbit in R4

2018 ◽  
Vol 76 (5) ◽  
pp. 1139-1160 ◽  
Author(s):  
Yuanyong Wu ◽  
Haibin Xiao
Keyword(s):  
Density Dependence ◽  
Traveling Wave ◽  
Heteroclinic Orbit ◽  
Traveling Wave Solutions ◽  
Predator Prey ◽  
Wave Solutions

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.

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

Traveling wave solutions in predator–prey models with competition

2021 ◽  
Author(s):  
Guo Lin ◽  
Yibing Xing
Keyword(s):  
Traveling Wave ◽  
Wave Speed ◽  
Traveling Wave Solutions ◽  
Initial Value ◽  
Predator Prey ◽  
Wave Solutions ◽  
Minimal Wave Speed ◽  
Predator Prey Models ◽  
Scalar Equations ◽  
Asymptotic Spreading

This paper studies the minimal wave speed of traveling wave solutions in predator–prey models, in which there are several groups of predators that compete among different groups. We investigate the existence and nonexistence of traveling wave solutions modeling the invasion of predators and coexistence of these species. When the positive solution of the corresponding kinetic system converges to the unique positive steady state, a threshold that is the minimal wave speed of traveling wave solutions is obtained. To finish the proof, we construct contracting rectangles and upper–lower solutions and apply the asymptotic spreading theory of scalar equations. Moreover, multiple propagation thresholds in the corresponding initial value problem are presented by numerical examples, and one threshold may be the minimal wave speed of traveling wave solutions.

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