Mathematical analysis of a food chain: prey - predator - biological - control
In this work, we present the dynamics of biological control through a mathematical model using a simple food chain of three trophic levels. This mathematical model is based on a ratio-dependent predator-prey model with Holling type II functional response, adding a top predator so this model is a sy...
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Universidad Nacional de Trujillo
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doaj-4cf19dfbdd994571ae55007d2c50e33a2020-11-24T23:28:37ZspaUniversidad Nacional de TrujilloSelecciones Matemáticas2411-17832017-07-014111212310.17268/sel.mat.2017.01.11Mathematical analysis of a food chain: prey - predator - biological - controlJhelly Pérez Nuñez0Roxana López Cruz1Departamento de Matemáticas, Universidad Nacional Mayor de San Marcos, Av. Venezuela s/n., Ciudad Universitaria, Lima-PerúDepartamento de Matemáticas, Universidad Nacional Mayor de San Marcos, Av. Venezuela s/n., Ciudad Universitaria, Lima-PerúIn this work, we present the dynamics of biological control through a mathematical model using a simple food chain of three trophic levels. This mathematical model is based on a ratio-dependent predator-prey model with Holling type II functional response, adding a top predator so this model is a system of three ordinary differential equations. We study the existence and uniqueness, invariance and boundary of solutions. The information given in this work could also be useful for the design of development plans that meet the needs of the agricultural sector to guide the non-pollution of the environment in the country through the use of biological control to control pests.http://revistas.unitru.edu.pe/index.php/SSMM/article/view/1433/1444Predator - PreyFood ChainBiological ControlScenarios ExtinctionAsymptotic StabilityRunge - Kutta |
collection |
DOAJ |
language |
Spanish |
format |
Article |
sources |
DOAJ |
author |
Jhelly Pérez Nuñez Roxana López Cruz |
spellingShingle |
Jhelly Pérez Nuñez Roxana López Cruz Mathematical analysis of a food chain: prey - predator - biological - control Selecciones Matemáticas Predator - Prey Food Chain Biological Control Scenarios Extinction Asymptotic Stability Runge - Kutta |
author_facet |
Jhelly Pérez Nuñez Roxana López Cruz |
author_sort |
Jhelly Pérez Nuñez |
title |
Mathematical analysis of a food chain: prey - predator - biological - control |
title_short |
Mathematical analysis of a food chain: prey - predator - biological - control |
title_full |
Mathematical analysis of a food chain: prey - predator - biological - control |
title_fullStr |
Mathematical analysis of a food chain: prey - predator - biological - control |
title_full_unstemmed |
Mathematical analysis of a food chain: prey - predator - biological - control |
title_sort |
mathematical analysis of a food chain: prey - predator - biological - control |
publisher |
Universidad Nacional de Trujillo |
series |
Selecciones Matemáticas |
issn |
2411-1783 |
publishDate |
2017-07-01 |
description |
In this work, we present the dynamics of biological control through a mathematical model using a simple food chain of three trophic levels. This mathematical model is based on a ratio-dependent
predator-prey model with Holling type II functional response, adding a top predator so this model is a system of three ordinary differential equations. We study the existence and uniqueness, invariance and boundary of solutions. The information given in this work could also be useful for the design of development plans that meet the needs of the agricultural sector to guide the non-pollution of the environment in the country through the use of biological control to control pests. |
topic |
Predator - Prey Food Chain Biological Control Scenarios Extinction Asymptotic Stability Runge - Kutta |
url |
http://revistas.unitru.edu.pe/index.php/SSMM/article/view/1433/1444 |
work_keys_str_mv |
AT jhellypereznunez mathematicalanalysisofafoodchainpreypredatorbiologicalcontrol AT roxanalopezcruz mathematicalanalysisofafoodchainpreypredatorbiologicalcontrol |
_version_ |
1725548836365008896 |