Bifurcation and control of a bioeconomic model of a prey-predator system with a time delay
type: Item
instance of: scholarly article
title: Bifurcation and control of a bioeconomic model of a prey-predator system with a time delay
zbMATH Open document ID: 1245.92060
author: Kunal Chakraborty
author: Milon Chakraborty
author: T. K. Kar
published in: Nonlinear Analysis. Hybrid Systems
publication date: 2011-11-03T00:00:00Z
review text: The dynamical behaviour of a bioeconomic model system of differential algebraic equations is analysed. The system describes a prey-predator fishery with two zones (free fishing and protected). It is shown that a singularity-induced bifurcation occurs when a variation of economic interest of harvesting is considered, thus the interior equilibrium changes from being stable to being unstable. A sufficient condition is obtained for the interior equilibrium to be stable when a state feedback controller is introduced. Further, when the time delay is incorporated as a parameter, Hopf bifurcation also occurs. Then these results are verified by some numerical simulations.
reviewed by: Zhanyuan Hou
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 91B76
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 65C20
zbMATH DE Number: 5967331
zbMATH Keywords: fishery
zbMATH Keywords: differential algebraic system
zbMATH Keywords: Hopf bifurcations
MaRDI profile type: Publication
full work available at URL: j.nahs.2011.05.004
OpenAlex ID: W1966880675
Wikidata QID: Q115568750
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DOI: 10.1016/J.NAHS.2011.05.004
description: scientific article; zbMATH DE number 5967331