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arXiv · 2007.02568

Asymptotic spreading speeds for a predator-prey system with two predators and one prey

Arnaud Ducrot·Thomas Giletti·Jong-Shenq Guo·Masahiko Shimojo
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Abstract

This paper investigates the large time behaviour of a three species reaction-diffusion system, modelling the spatial invasion of two predators feeding on a single prey species. In addition to the competition for food, the two predators exhibit competitive interactions and under some parameter conditions ($\mu>0$), they can also be considered as two mutants. When mutations occur in the predator populations, the spatial spread of invasion takes place at a definite speed, identical for both mutants. When the two predators are not coupled through mutation, the spreading behaviour exhibits a more complex propagating pattern, including multiple layers with different speeds. In addition, some parameter conditions reveal situations where a nonlocal pulling phenomenon occurs and in particular where the spreading speed is not linearly determined.

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Arnaud Ducrot, Thomas Giletti, Jong-Shenq Guo, Masahiko Shimojo. 2020-07-06. Asymptotic spreading speeds for a predator-prey system with two predators and one prey. https://arxiv.org/abs/2007.02568

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