Persistence of preys in a diffusive three species predator-prey system with a pair of strong-weak competing preys

We investigate the traveling wave solutions of a three-species system involving a single predator and a pair of strong-weak competing preys. Our results show how the predation may affect this dynamics. More precisely, we describe several situations where the environment is initially inhabited by the predator and by either one of the two preys. When the weak competing prey is an aboriginal species, we show that there exist traveling waves where the strong prey invades the environment and either replaces its weak counterpart, or more surprisingly the three species eventually co-exist. Furthermore, depending on the parameters, we can also construct traveling waves where the weaker prey actually invades the environment initially inhabited by its strong competitor and the predator. In all those situations, we find the infimum of the set of admissible wave speeds; these results are sharp at least when the three species diffusive at the same speed. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

This study investigates traveling wave solutions of a three-species system involving a predator and competing preys, demonstrating how predation affects the dynamics. The results show various scenarios where one prey species invades, replaces, or coexists with the others. Additionally, it is found that under certain parameters, the weaker prey can invade environments initially occupied by stronger competitors. The study also determines the infimum of admissible wave speeds, particularly when all three species diffuse at the same rate.