Population dynamics with protection and harvesting of a species

Christian Camilo Cortes; Juan David Hernandez

doi:10.15446/recolma.v56n2.108369

Publicado

2023-04-17

Population dynamics with protection and harvesting of a species

Dinámica poblacional con protección y explotación de una especie

DOI:

https://doi.org/10.15446/recolma.v56n2.108369

Palabras clave:

Filipov systems, bifurcation, sliding segment, Poincare- Bendixson criteria, limit cycle (en)
Sistemas de Filippov, Bifurcación, segmento deslizante, criterio de Poincare-Bendinxson, ciclo limite (es)

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Autores/as

Christian Camilo Cortes Universidad Carlos III de Madrid
Juan David Hernandez Universidad Surcolombiana

Resumen (en)
Resumen (es)

In this work we study the dynamics associated to the interaction of juveniles and adults of the same species, where the harvesting of adults is not allowed when the number of adults is below a critical value. This study is carried out by bifurcation analysis, for a Filippov system, in relation to two parameters: harvesting and protection of the adult species.

En este trabajo se estudia la dinámica entre la interacción de jóvenes y adultos de una misma especie, donde la explotación de los adultos no es permitida cuando el número de adultos es inferior a un valor crítico. Este estudio es llevado a cabo por el análisis de bifurcación, para un sistema de Filippov, con relación a dos parámetros: explotación y protección de la especie adulta.

Referencias

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L. Edelstein-Keshet, Mathematical models in biology, SIAM, 2005. DOI: https://doi.org/10.1137/1.9780898719147

A. F. Filippov, Differential equations with discontinuous righthand sides: control systems, vol. 18, Springer Science & Business Media, 2013.

C. Cortes Garcia, Bifurcaciones en modelo gause depredador-presa con discontinuidad, Revista de Matemática: Teoría y Aplicaciones 28 (2021), no. 2, 183-208. DOI: https://doi.org/10.15517/rmta.v28i2.36084

M. Guardia, T. M. Seara, and M. A. Teixeira, Generic bifurcations of low codimension of planar Filippov systems, Journal of Differential Equations 250 (2011), no. 4, 1967-2023. DOI: https://doi.org/10.1016/j.jde.2010.11.016

Y. A. Kuznetsov, Elements of applied bifurcation theory, vol. 112, Springer Science & Business Media, 2013.

Y. A. Kuznetsov, S. Rinaldi, and A. Gragnani, One-parameter bifurcations in planar Filippov systems, International Journal of Bifurcation and chaos 13 (2003), no. 08, 2157-2188. DOI: https://doi.org/10.1142/S0218127403007874

J. D. Murray, Mathematical biology: I. an introduction, vol. 17, Springer Science & Business Media, 2007.

J. Sotomayor, Licoes de equacoes diferenciais ordinárias (vol. 11), Instituto de Matemática Pura e Aplicada, CNPq (1979).

Cómo citar

APA

Cortes, C. C. y Hernandez, J. D. (2023). Population dynamics with protection and harvesting of a species. Revista Colombiana de Matemáticas, 56(2), 113–131. https://doi.org/10.15446/recolma.v56n2.108369

ACM

[1]

Cortes, C.C. y Hernandez, J.D. 2023. Population dynamics with protection and harvesting of a species. Revista Colombiana de Matemáticas. 56, 2 (abr. 2023), 113–131. DOI:https://doi.org/10.15446/recolma.v56n2.108369.

ACS

(1)

Cortes, C. C.; Hernandez, J. D. Population dynamics with protection and harvesting of a species. rev.colomb.mat 2023, 56, 113-131.

ABNT

CORTES, C. C.; HERNANDEZ, J. D. Population dynamics with protection and harvesting of a species. Revista Colombiana de Matemáticas, [S. l.], v. 56, n. 2, p. 113–131, 2023. DOI: 10.15446/recolma.v56n2.108369. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/108369. Acesso em: 22 ene. 2025.

Chicago

Cortes, Christian Camilo, y Juan David Hernandez. 2023. «Population dynamics with protection and harvesting of a species». Revista Colombiana De Matemáticas 56 (2):113-31. https://doi.org/10.15446/recolma.v56n2.108369.

Harvard

Cortes, C. C. y Hernandez, J. D. (2023) «Population dynamics with protection and harvesting of a species», Revista Colombiana de Matemáticas, 56(2), pp. 113–131. doi: 10.15446/recolma.v56n2.108369.

IEEE

[1]

C. C. Cortes y J. D. Hernandez, «Population dynamics with protection and harvesting of a species», rev.colomb.mat, vol. 56, n.º 2, pp. 113–131, abr. 2023.

MLA

Cortes, C. C., y J. D. Hernandez. «Population dynamics with protection and harvesting of a species». Revista Colombiana de Matemáticas, vol. 56, n.º 2, abril de 2023, pp. 113-31, doi:10.15446/recolma.v56n2.108369.

Turabian

Cortes, Christian Camilo, y Juan David Hernandez. «Population dynamics with protection and harvesting of a species». Revista Colombiana de Matemáticas 56, no. 2 (abril 17, 2023): 113–131. Accedido enero 22, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/108369.

Vancouver

1.

Cortes CC, Hernandez JD. Population dynamics with protection and harvesting of a species. rev.colomb.mat [Internet]. 17 de abril de 2023 [citado 22 de enero de 2025];56(2):113-31. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/108369

Descargar cita

CrossRef Cited-by

3

1. Christian Cortés García, Jasmidt Vera Cuenca. (2023). Impact of alternative food on predator diet in a Leslie-Gower model with prey refuge and Holling Ⅱ functional response. Mathematical Biosciences and Engineering, 20(8), p.13681. https://doi.org/10.3934/mbe.2023610.

2. Christian Cortés-García. (2025). Population dynamics in a Leslie-Gower predator-prey model with proportional prey refuge at low densities. Journal of Mathematical Analysis and Applications, 543(2), p.128993. https://doi.org/10.1016/j.jmaa.2024.128993.

3. Christian Cortés García. (2025). Population dynamics in a Leslie–Gower predator–prey model with predator harvesting at high densities. Mathematical Methods in the Applied Sciences, 48(1), p.804. https://doi.org/10.1002/mma.10359.