Flip bifurcation of a discrete predator-prey model with modified Leslie-Gower and Holling-type III schemes
type: Item
instance of: scholarly article
title: Flip bifurcation of a discrete predator-prey model with modified Leslie-Gower and Holling-type III schemes
zbMATH Open document ID: 1475.92134
published in: Mathematical Biosciences and Engineering
publication date: 2021-08-27T00:00:00Z
review text: In this paper, the authors transformed a continuous predator-prey model with modified Leslie-Gower and Holling-type III schemes into a discrete mode by using Euler approximation method. The existence and stability of fixed points for this discrete model were investigated. Flip bifurcation analyses of this discrete model was carried out and corresponding bifurcation conditions were obtained. Provided with these bifurcation conditions, an example was given to carry out numerical simulations, which shows that the discrete model undergoes flip bifurcation around the stable fixed point. In addition, compared with previous studies on the continuous predator-prey model, their discrete model shows more irregular and complex dynamic characteristics. The present research can be regarded as the continuation and development of the former studies [\textit{K. Liu} et al., Comput. Math. Methods Med. 2019, Article ID 3859815, 10 p. (2019; Zbl 1423.92198)].
reviewed by: Yingxin Guo
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 7387871
zbMATH Keywords: flip bifurcation
zbMATH Keywords: Euler approximation method
zbMATH Keywords: discrete predator-prey model
zbMATH Keywords: stability
zbMATH Keywords: center manifold theorem
author: Yangyang Li
author: Feng-Xue Zhang
author: Xianglai Zhuo
MaRDI profile type: Publication
full work available at URL: mbe.2020106
OpenAlex ID: W2996465988
Wikidata QID: Q90791887
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DOI: 10.3934/MBE.2020106
description: scientific article; zbMATH DE number 7387871