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

<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>

Author(s):  
Xinzhi Ren ◽  
Tianran Zhang ◽  
Xianning Liu

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.


2018 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Yu-Xia Hao ◽  
◽  
Wan-Tong Li ◽  
Fei-Ying Yang

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