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

<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>

Traveling wave solutions for a diffusive three-species intraguild predation model

The aim of this work is to investigate the existence and non-existence of traveling wave solutions for a diffusive three-species intraguild predation model which means that one predator can eat its potential resource competitors. The method of upper–lower solution is implemented to show the existence of traveling wave solutions. In order to simplify the construction of an admissible pair of upper–lower solution, the scheme of strictly contracting rectangle is applied. Finally, the minimal speed [Formula: see text] of traveling wave solutions of the model is characterized. If the wave speed is greater than [Formula: see text], we show the existence of traveling wave solutions connecting trivial and positive equilibria by combining the upper and lower solutions with the contracting rectangle. On the other hand, if the wave speed is less than [Formula: see text], the non-existence of such solutions is also established. Furthermore, to illustrate our theoretical results, some numerical simulations are performed and biological meanings are interpreted.