Mathematics Faculty Articles

Attraction–repulsion taxis mechanisms in a predator–prey model

Document Type

Article

Publication Date

4-14-2021

Publication Title

Partial Differential Equations and Applications

Keywords

Predator prey, Prey-taxis, Indirect taxis, Chemorepulsion, Pattern formation, Bifurcation, Stability

ISSN

2662-2971

Volume

2

Issue/No.

34

First Page

1

Last Page

29

Abstract

We consider a predator–prey model where the predator population favors the prey through biased diffusion toward the prey density, while the prey population employs a chemical repulsive mechanism. This leads to a quasilinear parabolic system. We first establish the global existence of positive solutions. Thereafter we show the existence of nontrivial steady state solutions via bifurcation theory, then we discuss the stability of these branch solutions. Through numerical simulation we analyze the nature of patterns formed and interpret results in terms of the survival and distribution of the two populations.

DOI

10.1007/s42985-021-00080-0

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