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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.52 no.1 Bogotá Jan./June 2018

https://doi.org/10.15446/recolma.v1n52.74564 

Original articles

Existence of Unique and Global Asymptotically Stable Almost Periodic Solution of a Discrete Predator-Prey System with Beddington-DeAngelis Functional Response and Density Dependent

Existencia de una única solución casi periódica global asintóticamente estable de un sistema Depredador-Presa con respuesta funcional Beddington-DeAngelis y densamente dependiente

Cosme Duque1  * 

1 Universidad de Los Andes, Mérida - Venezuela


Abstract:

The main concern of this paper is to study the dynamics of a discrete predator-prey system with Beddington-DeAngelis functional response and density dependent predator, assuming that the coefficients involved in the system are almost periodic. More concretely, under certain conditions, we prove the existence of a unique almost periodic solution which is globally attractive. We exhibit a few numerical examples of the results.

Keywords: Density dependent predator; Beddington-DeAngelis functional response; discrete predator-prey; almost periodic solution

Resumen:

El objetivo principal de este artículo es el de estudiar la dinámica de un sistema depredador-presa discreto con respuesta funcional Beddington-DeAngelis y densamente dependiente del depredador, asumiendo que los coeficientes involucrados en el sistema son casi periódicos. De forma más concreta, bajo ciertas condiciones, probaremos la existencia de una única solución casi periódica la cual es globalmente atractiva. Exhibimos algunos ejemplos numéricos de los resultados.

Palabras clave: Densamente dependiente depredador; respuesta funcional Beddington-DeAngelis; depredador-presa discreto; solución casi periódica

Text complete end PDF

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Received: June 05, 2017; Accepted: December 14, 2017

*Correspondencia: Cosme Duque, Departamento de Matemáticas, Universidad de Los Andes, Facultad de Ciencias, La Hechicera, Mérida - Venezuela. Correo electrónico: duquec@ula.ve. DOI: https://doi.org/10.15446/recolma.v1n52.74564

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