Research ArticleNo Access

Complex dynamics and bifurcation analysis for a Beverton–Holt population model with Allee effect

MRI Laboratory, Faculté Polydisciplinaire Khouribga, Sultan Moulay Slimane University, BP: 145 Khouribga Principale, 25000, Kingdom of Morocco

E-mail Address: moknirima@gmail.com

Corresponding author.

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Mohamed Ch-Chaoui

MRI Laboratory, Faculté Polydisciplinaire Khouribga, Sultan Moulay Slimane University, BP: 145 Khouribga Principale, 25000, Kingdom of Morocco

E-mail Address: m.chchaoui@usms.ma

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https://doi.org/10.1142/S1793524522501273Cited by:10 (Source: Crossref)

Abstract

In this paper, we have derived a discrete evolutionary Beverton–Holt population model. The model is built using evolutionary game theory methodology and takes into consideration the strong Allee effect related to predation saturation. We have discussed the existence of the positive fixed point and examined its asymptotic stability. Analytically, we demonstrated that the derived model exhibits Neimark–Sacker bifurcation when the maximal predator intensity is at lower values. All chaotic behaviors are justified numerically. Finally, to avoid these chaotic features and achieve asymptotic stability, we implement two chaos control methods.

Keywords:

AMSC: 39A13, 39A28, 9A30, 39A33, 37L10

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