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Memory and mutualism in species sustainability: A time-fractional Lotka-Volterra model with harvesting

We first present a predator-prey model for two species and then extend the model to three species where the two predator species engage in mutualistic predation. Constant effort harvesting and the impact of by-catch issue are also incorporated. Necessary sufficient conditions for the existence and s...

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Detalles Bibliográficos
Autores principales: Amirian, Mohammad M., Towers, I.N., Jovanoski, Z., Irwin, Andrew J.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7479346/
https://www.ncbi.nlm.nih.gov/pubmed/32939415
http://dx.doi.org/10.1016/j.heliyon.2020.e04816
Descripción
Sumario:We first present a predator-prey model for two species and then extend the model to three species where the two predator species engage in mutualistic predation. Constant effort harvesting and the impact of by-catch issue are also incorporated. Necessary sufficient conditions for the existence and stability of positive equilibrium points are examined. It is shown that harvesting is sustainable, and the memory concept of the fractional derivative damps out oscillations in the population numbers so that the system as a whole settles on an equilibrium quicker than it would with integer time derivatives. Finally, some possible physical explanations are given for the obtained results. It is shown that the stability requires the memory concept in the model.