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Predator invasion in predator–prey model with prey-taxis in spatially heterogeneous environment

Authors
Choi, W.Ahn, I.
Issue Date
6월-2022
Publisher
Elsevier Ltd
Keywords
Invasion; Local stability; Prey-taxis; Spatially heterogeneous environment
Citation
Nonlinear Analysis: Real World Applications, v.65
Indexed
SCIE
SCOPUS
Journal Title
Nonlinear Analysis: Real World Applications
Volume
65
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/137549
DOI
10.1016/j.nonrwa.2021.103495
ISSN
1468-1218
Abstract
We consider a predator–prey model with prey-taxis and Holling-type II functional responses in a spatially heterogeneous environment to analyze the effects of prey-taxis and the heterogeneity of an environment on predator invasion. To achieve our goal, we investigate the stability of semi-trivial solution in which the predator is absent. It is known that both the predator diffusion and the death rate contribute to the predator invasion in a heterogeneous habitat when there is no prey-taxis. In this paper, we show that predator invasion is affected by the prey-taxis and diffusions of the prey-taxis model for a certain range of predator death rates in a heterogeneous environment. Furthermore, in cases where predator invasion by predator diffusion does not occur in a particular death rate range of the predator, predator invasion can occur by prey-taxis in a spatially heterogeneous habitat. In addition, we compare this phenomenon to the corresponding predator–prey model with ratio-dependent functional responses. It is observed that none of the predator's diffusion and prey-taxis affect the predator's invasion, and that only the predator's death rate contributes to predator invasion for the model with ratio-dependent functional responses. © 2021 Elsevier Ltd
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