Prey-predator model in drainage system with migration and harvesting

In this paper, we consider a prey-predator model with a reserve region of predator where generalist predator cannot enter. Based on the intake capacity of food and other factors, we introduce the predator population which consumes the prey population with Holling type-II functional response; and gen...

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Autores principales:	Roy Banani, Roy Sankar Kumar
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	prey-predator system hopf bifurcation harvesting local and global stability optimal control 92b05 34c23 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/d8879dabef0648a8a8ae141201375308
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spelling	oai:doaj.org-article:d8879dabef0648a8a8ae1412013753082021-12-05T14:10:56ZPrey-predator model in drainage system with migration and harvesting2353-062610.1515/msds-2021-0131https://doaj.org/article/d8879dabef0648a8a8ae1412013753082021-06-01T00:00:00Zhttps://doi.org/10.1515/msds-2021-0131https://doaj.org/toc/2353-0626In this paper, we consider a prey-predator model with a reserve region of predator where generalist predator cannot enter. Based on the intake capacity of food and other factors, we introduce the predator population which consumes the prey population with Holling type-II functional response; and generalist predator population consumes the predator population with Beddington-DeAngelis functional response. The density-dependent mortality rate for prey and generalist predator are considered. The equilibria of proposed system are determined. Local stability for the system are discussed. The environmental carrying capacity is considered as a bifurcation parameter to evaluate Hopf bifurcation in the neighbourhood at an interior equilibrium point. Here the fishing effort is used as a control parameter to harvest the generalist predator population of the system. With the help of this control parameter, a dynamic framework is developed to investigate the optimal utilization of resources, sustainability properties of the stock and the resource rent. Finally, we present a numerical simulation to verify the analytical results, and the system is analyzed through graphical illustrations. The main findings with future research directions are described at last.Roy BananiRoy Sankar KumarDe Gruyterarticleprey-predator systemhopf bifurcationharvestinglocal and global stabilityoptimal control92b0534c23MathematicsQA1-939ENNonautonomous Dynamical Systems, Vol 8, Iss 1, Pp 152-167 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	prey-predator system hopf bifurcation harvesting local and global stability optimal control 92b05 34c23 Mathematics QA1-939
spellingShingle	prey-predator system hopf bifurcation harvesting local and global stability optimal control 92b05 34c23 Mathematics QA1-939 Roy Banani Roy Sankar Kumar Prey-predator model in drainage system with migration and harvesting
description	In this paper, we consider a prey-predator model with a reserve region of predator where generalist predator cannot enter. Based on the intake capacity of food and other factors, we introduce the predator population which consumes the prey population with Holling type-II functional response; and generalist predator population consumes the predator population with Beddington-DeAngelis functional response. The density-dependent mortality rate for prey and generalist predator are considered. The equilibria of proposed system are determined. Local stability for the system are discussed. The environmental carrying capacity is considered as a bifurcation parameter to evaluate Hopf bifurcation in the neighbourhood at an interior equilibrium point. Here the fishing effort is used as a control parameter to harvest the generalist predator population of the system. With the help of this control parameter, a dynamic framework is developed to investigate the optimal utilization of resources, sustainability properties of the stock and the resource rent. Finally, we present a numerical simulation to verify the analytical results, and the system is analyzed through graphical illustrations. The main findings with future research directions are described at last.
format	article
author	Roy Banani Roy Sankar Kumar
author_facet	Roy Banani Roy Sankar Kumar
author_sort	Roy Banani
title	Prey-predator model in drainage system with migration and harvesting
title_short	Prey-predator model in drainage system with migration and harvesting
title_full	Prey-predator model in drainage system with migration and harvesting
title_fullStr	Prey-predator model in drainage system with migration and harvesting
title_full_unstemmed	Prey-predator model in drainage system with migration and harvesting
title_sort	prey-predator model in drainage system with migration and harvesting
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/d8879dabef0648a8a8ae141201375308
work_keys_str_mv	AT roybanani preypredatormodelindrainagesystemwithmigrationandharvesting AT roysankarkumar preypredatormodelindrainagesystemwithmigrationandharvesting
_version_	1718371571672809472

Prey-predator model in drainage system with migration and harvesting

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