Spatiotemporal complexity of a Leslie-Gower predator-prey model with the weak Allee effect
type: Item
instance of: scholarly article
title: Spatiotemporal complexity of a Leslie-Gower predator-prey model with the weak Allee effect
zbMATH Open document ID: 1397.92563
DOI: 10.1155/2013/535746
author: Yongli Cai
author: Caidi Zhao
author: Weiming Wang
published in: Journal of Applied Mathematics
publication date: 2018-10-10T00:00:00Z
review text: Summary: We investigate a diffusive Leslie-Gower predator-prey model with the additive Allee effect on prey subject to the zero-flux boundary conditions. Some results of solutions to this model and its corresponding steady-state problem are shown. More precisely, we give the stability of the positive constant steady-state solution, the refined a priori estimates of positive solution, and the nonexistence and existence of the positive nonconstant solutions. We carry out the analytical study for two-dimensional system in detail and find out the certain conditions for Turing instability. Furthermore, we perform numerical simulations and show that the model exhibits a transition from stripe-spot mixtures growth to isolated spots and also to stripes. These results show that the impact of the Allee effect essentially increases the model spatiotemporal complexity.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 6950732
zbMATH Keywords: Leslie-Gower predator-prey model
zbMATH Keywords: Allee effect
zbMATH Keywords: Turing instability
Wikidata QID: Q59002885
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/535746
OpenAlex ID: W2090196983
DBLP publication ID: journals/jam/CaiZW13
description: scientific article; zbMATH DE number 6950732