Population Dynamics with Density-Dependent Immigrations and Allee eﬀect

Ossandón, Gustavo A.; Castro Santis, Ricardo; Ossandón, Gustavo A.; Castro Santis, Ricardo

doi:10.15446/recolma.v52n2.77160

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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.52 no.2 Bogotá Jul./Dec. 2018

https://doi.org/10.15446/recolma.v52n2.77160

Original articles

Population Dynamics with Density-Dependent Immigrations and Allee eﬀect

Dinámica de Poblaciones con Inmigración Denso-Dependiente y Efecto Allee

Gustavo A. Ossandón¹^*

Ricardo Castro Santis²

^¹ Universidad Tecnológica Metropolitana, Departamento de Matemáticas, Las Palmeras 3232, Ñuñoa, Chile. e-mail: gusosar@utem.cl

^² Universidad Tecnológica Metropolitana, Departamento de Matemáticas, Las Palmeras 3232, Ñuñoa, Chile. e-mail: e-mail: rcastro@utem.cl

Abstract

This study assesses the eﬀects of migration on the dynamics of a species population. It is considered that the species in its natural state and without the presence of migration exhibits Allee eﬀect. This work also considers migration as a density-dependent function, which, from a maximum rate, decreases to a minimum of zero when the population reaches its carrying capacity.

Keywords: Population Dynamics with; Density-Dependent Immigrations and; Allee eﬀect

Resumen

Este trabajo estudia los efectos de la inmigración sobre la dinámica poblacional de una especie. Se considerará que la especie en estado natural y sin la presencia de migraciones presenta efecto Allee. En este trabajo se considerará además la inmigración como una función denso dependiente, que, partiendo de una tasa máxima, disminuye a un mínimo de cero cuando la población alcance su capacidad de carga.

Palabras clave: Dinámica de Poblaciones; con inmigración denso-dependiente; y efecto Allee

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Referencias

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[3] C. W. Clark, Mathematical Bioeconomic: The optimal management of renovavle resources, second edition, fourth ed., Addison-Wesley Publishing Company, 1990. [ Links ]

[4] B. Dennis, Allee eﬀects: population growth, critical density, and chance of extinction., Nat. Resour. Model. 3 (1989), 381-538. [ Links ]

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[6] E. Liz and A. Ruiz-Herrera, Delayed population models with Allee eﬀects and exploitation, Math. Biosci. Eng. 12 (2015). [ Links ]

[7] S. Petrovskii and B. Li, Mathematical Biosciences (2003), no. 1, 79-91. [ Links ]

Received: February 18, 2018; Accepted: August 13, 2018

^* Correspondencia: Gustavo A. Ossandón, Departamento de Matemáticas, Universidad Tecnológica Metropolitana, Las Palmeras 3232, Ñuñoa, Chile. Correo electrónico: gusosar@utem.cl.

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