Bifurcation analysis and control of a differential-algebraic predator-prey model with Allee effect and time delay
type: Item
instance of: scholarly article
title: Bifurcation analysis and control of a differential-algebraic predator-prey model with Allee effect and time delay
zbMATH Open document ID: 1406.92541
DOI: 10.1155/2014/107565
author: Xue Zhang
author: Qingling Zhang
published in: Journal of Applied Mathematics
publication date: 2019-02-01T00:00:00Z
review text: Summary: This paper studies systematically a differential-algebraic prey-predator model with time delay and Allee effect. It shows that transcritical bifurcation appears when a variation of predator handling time is taken into account. This model also exhibits singular induced bifurcation as the economic revenue increases through zero, which causes impulsive phenomenon. It can be noted that the impulsive phenomenon can be much weaker by strengthening Allee effect in numerical simulation. On the other hand, at a critical value of time delay, the model undergoes a Hopf bifurcation; that is, the increase of time delay destabilizes the model and bifurcates into small amplitude periodic solution. Moreover, a state delayed feedback control method, which can be implemented by adjusting the harvesting effort for biological populations, is proposed to drive the differential-algebraic system to a steady state. Finally, by using Matlab software, numerical simulations illustrate the effectiveness of the results.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 7010544
Wikidata QID: Q59049390
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/107565
OpenAlex ID: W2092092070
DBLP publication ID: journals/jam/ZhangZ14
description: scientific article; zbMATH DE number 7010544