Analysis of a Prey-Predator Fishing Model for Harvesting with The Limited Effect of Density and Toxicity

Analysis of a Prey-Predator Fishing Model for Harvesting with The Limited Effect of Density and Toxicity

We proposed a model of prey-predator fishing by considering proportion of prey density and toxicity in ecosystem. The model is analysed to study about biological equilibrium, bionomic equilibrium and its stability. The aim of the model is to determine the optimal sustainable harvesting for each spec...

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Main Authors: Dita Anies Munawwaroh, Sutimin, Siti Khabibah
Format: Article
Language:English
Published: EDP Sciences 2018-01-01
Series:E3S Web of Conferences
Subjects:
Prey-predator
harvesting
equilibrium
stability
Online Access:https://doi.org/10.1051/e3sconf/20187306001
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spelling doaj-335b81dde1ed43a8a6c8d047adfbb6432021-02-02T07:47:47ZengEDP SciencesE3S Web of Conferences2267-12422018-01-01730600110.1051/e3sconf/20187306001e3sconf_icenis18_06001Analysis of a Prey-Predator Fishing Model for Harvesting with The Limited Effect of Density and ToxicityDita Anies Munawwaroh0Sutimin1Siti Khabibah2Departement of Mathematics, Faculty of Sciences and Mathematics, Universitas DiponegoroDepartement of Mathematics, Faculty of Sciences and Mathematics, Universitas DiponegoroDepartement of Mathematics, Faculty of Sciences and Mathematics, Universitas DiponegoroWe proposed a model of prey-predator fishing by considering proportion of prey density and toxicity in ecosystem. The model is analysed to study about biological equilibrium, bionomic equilibrium and its stability. The aim of the model is to determine the optimal sustainable harvesting for each species. The optimal harvesting is resulted from Pontryagin’s maximal principle. The global stability of coexistence equilibrium is analyzed from Lyapunov function. The effect of toxicity leads to the decreasing of sustainable harvesting.https://doi.org/10.1051/e3sconf/20187306001Prey-predatorharvestingequilibriumstability
collection DOAJ
language English
format Article
sources DOAJ
author Dita Anies Munawwaroh
Sutimin
Siti Khabibah
spellingShingle Dita Anies Munawwaroh
Sutimin
Siti Khabibah
Analysis of a Prey-Predator Fishing Model for Harvesting with The Limited Effect of Density and Toxicity
E3S Web of Conferences
Prey-predator
harvesting
equilibrium
stability
author_facet Dita Anies Munawwaroh
Sutimin
Siti Khabibah
author_sort Dita Anies Munawwaroh
title Analysis of a Prey-Predator Fishing Model for Harvesting with The Limited Effect of Density and Toxicity
title_short Analysis of a Prey-Predator Fishing Model for Harvesting with The Limited Effect of Density and Toxicity
title_full Analysis of a Prey-Predator Fishing Model for Harvesting with The Limited Effect of Density and Toxicity
title_fullStr Analysis of a Prey-Predator Fishing Model for Harvesting with The Limited Effect of Density and Toxicity
title_full_unstemmed Analysis of a Prey-Predator Fishing Model for Harvesting with The Limited Effect of Density and Toxicity
title_sort analysis of a prey-predator fishing model for harvesting with the limited effect of density and toxicity
publisher EDP Sciences
series E3S Web of Conferences
issn 2267-1242
publishDate 2018-01-01
description We proposed a model of prey-predator fishing by considering proportion of prey density and toxicity in ecosystem. The model is analysed to study about biological equilibrium, bionomic equilibrium and its stability. The aim of the model is to determine the optimal sustainable harvesting for each species. The optimal harvesting is resulted from Pontryagin’s maximal principle. The global stability of coexistence equilibrium is analyzed from Lyapunov function. The effect of toxicity leads to the decreasing of sustainable harvesting.
topic Prey-predator
harvesting
equilibrium
stability
url https://doi.org/10.1051/e3sconf/20187306001
work_keys_str_mv AT ditaaniesmunawwaroh analysisofapreypredatorfishingmodelforharvestingwiththelimitedeffectofdensityandtoxicity
AT sutimin analysisofapreypredatorfishingmodelforharvestingwiththelimitedeffectofdensityandtoxicity
AT sitikhabibah analysisofapreypredatorfishingmodelforharvestingwiththelimitedeffectofdensityandtoxicity
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