Existence, multiplicity, and stability of positive solutions of a predator-prey model with dinosaur functional response
type: Item
instance of: scholarly article
title: Existence, multiplicity, and stability of positive solutions of a predator-prey model with dinosaur functional response
zbMATH Open document ID: 1426.34031
DOI: 10.1155/2017/4912032
author: Kenan Shi
author: Tongqian Zhang
author: Xiaozhou Feng
author: Jian-hui Tian
published in: Mathematical Problems in Engineering
publication date: 2018-11-05T00:00:00Z
review text: Summary: We investigate the property of positive solutions of a predator-prey model with Dinosaur functional response under Dirichlet boundary conditions. Firstly, using the comparison principle and fixed point index theory, the sufficient conditions and necessary conditions on coexistence of positive solutions of a predator-prey model with Dinosaur functional response are established. Secondly, by virtue of bifurcation theory, perturbation theory of eigenvalues, and the fixed point index theory, we establish the bifurcation of positive solutions of the model and obtain the stability and multiplicity of the positive solution under certain conditions. Furthermore, the local uniqueness result is studied when \(b\) and \(d\) are small enough. Finally, we investigate the multiplicity, uniqueness, and stability of positive solutions when \(k > 0\) is sufficiently large.
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 6972152
Wikidata QID: Q115522040
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/4912032
OpenAlex ID: W2744923734
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description: scientific article; zbMATH DE number 6972152