On the invariant rational curves of a certain family of polynomial differential equations

Homero Díaz-Marín; Osvaldo Osuna

doi:10.15446/recolma.v56n1.105621

Publicado

2022-11-02

On the invariant rational curves of a certain family of polynomial differential equations

Sobre las curvas racionales invariantes de cierta familia de ecuaciones diferenciales

DOI:

https://doi.org/10.15446/recolma.v56n1.105621

Palabras clave:

algebraic limit-cycles, Puiseux series, Newton polygon, predator-prey models, functional-response (en)
ciclos límte algebraicos, series de Puiseux, polígono de Newton, modelos depredador-presa, funcional de respuesta (es)

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Autores/as

Homero Díaz-Marín Universidad Michoacana
Osvaldo Osuna Universidad Michoacana

Resumen (en)
Resumen (es)

In this work, we present sufficient conditions to determine if the limit cycles of certain differential systems in the plane are algebraic or not. In particular, we obtain criteria such that the limit cycles of equations derived from predatory prey models with rational functional response are necessarily transcendental ovals.

En este trabajo presentamos condiciones necesarias y suficientes para determinar si los ciclos límite de ciertas ecuaciones diferenciales en el plano son algebraicos o no. Particularmente, obtenemos criterios para que ciclos límite de ciertas ecuaciones derivadas de modelos depredador - presa con ciertos funcionales racionales de respuesta sean necesariamente óvalos trascendentes.

Referencias

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Cómo citar

APA

Díaz-Marín, H. y Osuna, O. (2022). On the invariant rational curves of a certain family of polynomial differential equations. Revista Colombiana de Matemáticas, 56(1), 93–111. https://doi.org/10.15446/recolma.v56n1.105621

ACM

[1]

Díaz-Marín, H. y Osuna, O. 2022. On the invariant rational curves of a certain family of polynomial differential equations. Revista Colombiana de Matemáticas. 56, 1 (nov. 2022), 93–111. DOI:https://doi.org/10.15446/recolma.v56n1.105621.

ACS

(1)

Díaz-Marín, H.; Osuna, O. On the invariant rational curves of a certain family of polynomial differential equations. rev.colomb.mat 2022, 56, 93-111.

ABNT

DÍAZ-MARÍN, H.; OSUNA, O. On the invariant rational curves of a certain family of polynomial differential equations. Revista Colombiana de Matemáticas, [S. l.], v. 56, n. 1, p. 93–111, 2022. DOI: 10.15446/recolma.v56n1.105621. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/105621. Acesso em: 9 mar. 2025.

Chicago

Díaz-Marín, Homero, y Osvaldo Osuna. 2022. «On the invariant rational curves of a certain family of polynomial differential equations». Revista Colombiana De Matemáticas 56 (1):93-111. https://doi.org/10.15446/recolma.v56n1.105621.

Harvard

Díaz-Marín, H. y Osuna, O. (2022) «On the invariant rational curves of a certain family of polynomial differential equations», Revista Colombiana de Matemáticas, 56(1), pp. 93–111. doi: 10.15446/recolma.v56n1.105621.

IEEE

[1]

H. Díaz-Marín y O. Osuna, «On the invariant rational curves of a certain family of polynomial differential equations», rev.colomb.mat, vol. 56, n.º 1, pp. 93–111, nov. 2022.

MLA

Díaz-Marín, H., y O. Osuna. «On the invariant rational curves of a certain family of polynomial differential equations». Revista Colombiana de Matemáticas, vol. 56, n.º 1, noviembre de 2022, pp. 93-111, doi:10.15446/recolma.v56n1.105621.

Turabian

Díaz-Marín, Homero, y Osvaldo Osuna. «On the invariant rational curves of a certain family of polynomial differential equations». Revista Colombiana de Matemáticas 56, no. 1 (noviembre 2, 2022): 93–111. Accedido marzo 9, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/105621.

Vancouver

1.

Díaz-Marín H, Osuna O. On the invariant rational curves of a certain family of polynomial differential equations. rev.colomb.mat [Internet]. 2 de noviembre de 2022 [citado 9 de marzo de 2025];56(1):93-111. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/105621