The spreading speed and the minimal wave speed of a predator–prey system with nonlocal dispersal

2019 ◽  
Vol 70 (5) ◽  
Author(s):  
Arnaud Ducrot ◽  
Jong-Shenq Guo ◽  
Guo Lin ◽  
Shuxia Pan
Keyword(s):  
Wave Speed ◽  
Spreading Speed ◽  
Nonlocal Dispersal ◽  
Predator Prey ◽  
Prey System ◽  
Minimal Wave Speed

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 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.

Invasion waves for a diffusive predator–prey model with two preys and one predator

2020 ◽  
pp. 2050081
Author(s):  
Xinzhi Ren ◽  
Tianran Zhang ◽  
Xianning Liu
Keyword(s):  
Fixed Point ◽  
Wave Speed ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Traveling Fronts ◽  
Prey Model ◽  
Traveling Front ◽  
Minimal Wave Speed ◽  
Invasion Waves ◽  
Coexistence Equilibrium

In this paper, we study the existence of invasion waves of a diffusive predator–prey model with two preys and one predator. The existence of traveling semi-fronts connecting invasion-free equilibrium with wave speed [Formula: see text] is obtained by Schauder’s fixed-point theorem, where [Formula: see text] is the minimal wave speed. The boundedness of such waves is shown by rescaling method and such waves are proved to connect coexistence equilibrium by LaSalle’s invariance principle. The existence of traveling front with wave speed [Formula: see text] is got by rescaling method and limit arguments. The non-existence of traveling fronts with speed [Formula: see text] is shown by Laplace transform.

scholarly journals Invasion waves for a nonlocal dispersal predator-prey model with two predators and one prey

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Feiying Yang ◽  
Wantong Li ◽  
Renhu Wang
Keyword(s):  
Main Concern ◽  
Invasion Process ◽  
Nonlocal Dispersal ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Minimal Wave Speed ◽  
Contracting Rectangle ◽  
Invasion Waves ◽  
The Right

<p style='text-indent:20px;'>This paper is concerned with the propagation dynamics of a nonlocal dispersal predator-prey model with two predators and one prey. Precisely, our main concern is the invasion process of the two predators into the habitat of one prey, when the two predators are weak competitors in the absence of prey. This invasion process is characterized by the spreading speed of the predators as well as the minimal wave speed of traveling waves connecting the predator-free state to the co-existence state. Particularly, the right-hand tail limit of wave profile is derived by the idea of contracting rectangle.</p>

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.

Spreading speeds and travelling waves for non-monotone time-delayed lattice equations

2010 ◽  
Vol 466 (2119) ◽  
pp. 1919-1934 ◽  
Author(s):  
Jian Fang ◽  
Junjie Wei ◽  
Xiao-Qiang Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Wave Speed ◽  
Travelling Waves ◽  
Spreading Speed ◽  
Spreading Speeds ◽  
Minimal Wave Speed ◽  
Comparison Arguments ◽  
Fluctuation Method

A non-monotone time-delayed lattice system with global interaction is considered. The spreading speed, including the upward convergence, is established by comparison arguments and a fluctuation method. The existence of travelling waves is obtained by Schauder’s fixed-point theorem and a limiting process. It turns out that the minimal wave speed of travelling waves coincides with the spreading speed.

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