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Influence of the Collaboration Among Predators and the Weak Allee Effect on Prey in a Modified Leslie-Gower Predation Model

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Mathematical Methods for Engineering Applications (ICMASE 2022)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 414))

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Abstract

In this work, the behavior of the solutions of a bi-dimensional system of ordinary differential equations that models predator-prey interaction will be analyzed, obtained through a modification of the Leslie-Gower model, where the predator population considers hunting cooperation and the prey population is affected by a weak Allee effect. It is possible to find conditions for the coexistence of both species, as well as the possibility of periodic solutions, that imply oscillatory coexistence between species. We extend the properties already known for the case with a strong Allee effect and focus on the study of stability and local bifurcations.

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Author information

Authors and Affiliations

  1. Departamento de Matemáticas, Física y Estadística, Faculdad de Ciencias Básicas, Universidad Católica del Maule, Talca, Chile

    Alejandro Rojas-Palma

  2. Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile

    Eduardo González-Olivares

Authors
  1. Alejandro Rojas-Palma
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  2. Eduardo González-Olivares
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Corresponding author

Correspondence to Alejandro Rojas-Palma .

Editor information

Editors and Affiliations

  1. Faculty of Arts and Sciences, Ankara Hacı Bayram Veli University, Polatli, Ankara, Türkiye

    Fatih Yilmaz

  2. Department of Applied Mathematics, University of Salamanca, Salamanca, Spain

    Araceli Queiruga-Dios

  3. Department of Applied Mathematics, University of Salamanca, Salamanca, Spain

    Jesús Martín Vaquero

  4. Department of Mathematics and Computer Science, Technical University of Civil Engineering, Bucharest, Romania

    Ion Mierluş-Mazilu

  5. Department of Physics and Mathematics, Instituto Superior de Engenharia de Coimbra, Coimbra, Portugal

    Deolinda Rasteiro

  6. Centro Universitario de Tecnología y Arte Digital (U-tad) , Las Rozas de Madrid, Spain

    Víctor Gayoso Martínez

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Rojas-Palma, A., González-Olivares, E. (2023). Influence of the Collaboration Among Predators and the Weak Allee Effect on Prey in a Modified Leslie-Gower Predation Model. In: Yilmaz, F., Queiruga-Dios, A., Martín Vaquero, J., Mierluş-Mazilu, I., Rasteiro, D., Gayoso Martínez, V. (eds) Mathematical Methods for Engineering Applications. ICMASE 2022. Springer Proceedings in Mathematics & Statistics, vol 414. Springer, Cham. https://doi.org/10.1007/978-3-031-21700-5_15

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