Global stability and Hopf bifurcation for Gause-type predator-prey system
type: Item
instance of: scholarly article
title: Global stability and Hopf bifurcation for Gause-type predator-prey system
zbMATH Open document ID: 1248.34125
DOI: 10.1155/2012/260798
author: Shuang Guo
author: Weihua Jiang
published in: Journal of Applied Mathematics
publication date: 2012-08-06T00:00:00Z
review text: Summary: A class of three-dimensional Gause-type predator-prey models is considered. Firstly, local stability of the equilibrium indicating the extinction of top-predator is obtained. Secondly, we analyze the stability of the coexisting equilibrium of the predator-prey system with time delay when the predator catches the prey of pregnancy or with growth time. The delay can lead to periodic solutions, which is consistent with the law of growth for birds and some mammals. Further, an explicit formula is given which determines the stability of the bifurcating periodic solutions theoretically and the existence of periodic solutions is displayed by numerical simulations.
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K13
zbMATH DE Number: 6063343
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/260798
OpenAlex ID: W2070862490
Wikidata QID: Q58906498
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description: scientific article; zbMATH DE number 6063343