Limit Cycles in Predator-Prey Models
Descripción del Articulo
The classic Lotka-Volterra model belongs to a family of differential equations known as “Generalized Lotka-Volterra”, which is part of a classification of four models of quadratic fields with center. These models have been studied to address the Hilbert infinitesimal problem, which consists in deter...
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| Formato: | artículo |
| Fecha de Publicación: | 2017 |
| Institución: | Universidad Nacional de Trujillo |
| Repositorio: | Revistas - Universidad Nacional de Trujillo |
| Lenguaje: | español |
| OAI Identifier: | oai:ojs.revistas.unitru.edu.pe:article/1427 |
| Enlace del recurso: | https://revistas.unitru.edu.pe/index.php/SSMM/article/view/1427 |
| Nivel de acceso: | acceso abierto |
| Materia: | Limit Cycles Centers Hamiltonian Fields Ciclos límites centro campos hamiltonianos |
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Limit Cycles in Predator-Prey ModelsCiclos límites en modelos depredador-presaPuchuri Medina, LilianaLimit CyclesCentersHamiltonian FieldsCiclos límitescentrocampos hamiltonianosThe classic Lotka-Volterra model belongs to a family of differential equations known as “Generalized Lotka-Volterra”, which is part of a classification of four models of quadratic fields with center. These models have been studied to address the Hilbert infinitesimal problem, which consists in determine the number of limit cycles of a perturbed hamiltonian system with center. In this work, we first present an alternative proof of the existence of centers in Lotka-Volterra predator-prey models. This new approach is based in algebraic equations given by Kapteyn, which arose to answer Poincaré’s problem for quadratic fields. In addition, using Hopf Bifurcation theorem, we proof that more realistic models, obtained by a non-linear perturbation of a classic Lotka-Volterra model, also possess limit cycles.El modelo clásico de Lotka-Volterra pertenece a una familia de ecuaciones diferenciales denominada “Lotka-Volterra generalizado”, que forma parte de una clasificación de cuatro modelos de campos cuadráticos con centro. Estos modelos han sido estudiados para responder el problema infinitesimal de Hilbert, que consiste en determinar el número de ciclos límites que posee un sistema hamiltoniano perturbado y con centro. En este trabajo, en primer lugar presentamos una prueba alternativa de la existencia de centros en el modelo depredador-presa de Lotka-Volterra. Esta nueva prueba se basa en ecuaciones algebraicas dadas por Kapteyn, que surgieron para responder al problema de Poincaré para campos cuadráticos. En segundo lugar, usando el teorema de la bifurcación de Hopf, probamos que modelos depredador-presa más realistas, obtenidos por una pertubación no lineal del modelo de Lotka-Volterra clásico, poseen ciclos límites.National University of Trujillo - Academic Department of Mathematics2017-07-13info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdftext/htmlhttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/1427Selecciones Matemáticas; Vol. 4 Núm. 01 (2017): Enero - Julio; 70-81Selecciones Matemáticas; Vol. 4 No. 01 (2017): January - July; 70-81Selecciones Matemáticas; v. 4 n. 01 (2017): Enero - Julio; 70-812411-1783reponame:Revistas - Universidad Nacional de Trujilloinstname:Universidad Nacional de Trujilloinstacron:UNITRUspahttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/1427/2312https://revistas.unitru.edu.pe/index.php/SSMM/article/view/1427/2302Derechos de autor 2017 Selecciones Matemáticasinfo:eu-repo/semantics/openAccessoai:ojs.revistas.unitru.edu.pe:article/14272022-10-21T18:54:40Z |
| dc.title.none.fl_str_mv |
Limit Cycles in Predator-Prey Models Ciclos límites en modelos depredador-presa |
| title |
Limit Cycles in Predator-Prey Models |
| spellingShingle |
Limit Cycles in Predator-Prey Models Puchuri Medina, Liliana Limit Cycles Centers Hamiltonian Fields Ciclos límites centro campos hamiltonianos |
| title_short |
Limit Cycles in Predator-Prey Models |
| title_full |
Limit Cycles in Predator-Prey Models |
| title_fullStr |
Limit Cycles in Predator-Prey Models |
| title_full_unstemmed |
Limit Cycles in Predator-Prey Models |
| title_sort |
Limit Cycles in Predator-Prey Models |
| dc.creator.none.fl_str_mv |
Puchuri Medina, Liliana |
| author |
Puchuri Medina, Liliana |
| author_facet |
Puchuri Medina, Liliana |
| author_role |
author |
| dc.subject.none.fl_str_mv |
Limit Cycles Centers Hamiltonian Fields Ciclos límites centro campos hamiltonianos |
| topic |
Limit Cycles Centers Hamiltonian Fields Ciclos límites centro campos hamiltonianos |
| description |
The classic Lotka-Volterra model belongs to a family of differential equations known as “Generalized Lotka-Volterra”, which is part of a classification of four models of quadratic fields with center. These models have been studied to address the Hilbert infinitesimal problem, which consists in determine the number of limit cycles of a perturbed hamiltonian system with center. In this work, we first present an alternative proof of the existence of centers in Lotka-Volterra predator-prey models. This new approach is based in algebraic equations given by Kapteyn, which arose to answer Poincaré’s problem for quadratic fields. In addition, using Hopf Bifurcation theorem, we proof that more realistic models, obtained by a non-linear perturbation of a classic Lotka-Volterra model, also possess limit cycles. |
| publishDate |
2017 |
| dc.date.none.fl_str_mv |
2017-07-13 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
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article |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
https://revistas.unitru.edu.pe/index.php/SSMM/article/view/1427 |
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https://revistas.unitru.edu.pe/index.php/SSMM/article/view/1427 |
| dc.language.none.fl_str_mv |
spa |
| language |
spa |
| dc.relation.none.fl_str_mv |
https://revistas.unitru.edu.pe/index.php/SSMM/article/view/1427/2312 https://revistas.unitru.edu.pe/index.php/SSMM/article/view/1427/2302 |
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Derechos de autor 2017 Selecciones Matemáticas info:eu-repo/semantics/openAccess |
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Derechos de autor 2017 Selecciones Matemáticas |
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openAccess |
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application/pdf text/html |
| dc.publisher.none.fl_str_mv |
National University of Trujillo - Academic Department of Mathematics |
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National University of Trujillo - Academic Department of Mathematics |
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Selecciones Matemáticas; Vol. 4 Núm. 01 (2017): Enero - Julio; 70-81 Selecciones Matemáticas; Vol. 4 No. 01 (2017): January - July; 70-81 Selecciones Matemáticas; v. 4 n. 01 (2017): Enero - Julio; 70-81 2411-1783 reponame:Revistas - Universidad Nacional de Trujillo instname:Universidad Nacional de Trujillo instacron:UNITRU |
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Universidad Nacional de Trujillo |
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UNITRU |
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UNITRU |
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Revistas - Universidad Nacional de Trujillo |
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Revistas - Universidad Nacional de Trujillo |
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Nota importante:
La información contenida en este registro es de entera responsabilidad de la institución que gestiona el repositorio institucional donde esta contenido este documento o set de datos. El CONCYTEC no se hace responsable por los contenidos (publicaciones y/o datos) accesibles a través del Repositorio Nacional Digital de Ciencia, Tecnología e Innovación de Acceso Abierto (ALICIA).
La información contenida en este registro es de entera responsabilidad de la institución que gestiona el repositorio institucional donde esta contenido este documento o set de datos. El CONCYTEC no se hace responsable por los contenidos (publicaciones y/o datos) accesibles a través del Repositorio Nacional Digital de Ciencia, Tecnología e Innovación de Acceso Abierto (ALICIA).
