Research ArticleNo Access

Analytical bifurcation and strong resonances of a discrete Bazykin–Berezovskaya predator–prey model with Allee effect

Mathematics Department, Faculty of Education, Alexandria University, Alexandria, Egypt

and

Mathematics Department, College of Science and Humanities Studies in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

Department of Basic Science, Faculty of Computers and Informatics, Ismailia 41522, Suez Canal University, Egypt

E-mail Address: aelsadany1@yahoo.com

Corresponding author.

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https://doi.org/10.1142/S1793524522501364Cited by:3 (Source: Crossref)

Abstract

This paper investigates multiple bifurcations analyses and strong resonances of the Bazykin–Berezovskaya predator–prey model in depth using analytical and numerical bifurcation analysis. The stability conditions of fixed points, codim-1 and codim-2 bifurcations to include multiple and generic bifurcations are studied. This model exhibits transcritical, flip, Neimark–Sacker, and $1 : 2$ $1 : 2$ , $1 : 3$ $1 : 3$ , $1 : 4$ $1 : 4$ strong resonances. The normal form coefficients and their scenarios for each bifurcation are examined by using the normal form theorem and bifurcation theory. For each bifurcation, various types of critical states are calculated, such as potential transformations between the one-parameter bifurcation point and different bifurcation points obtained from the two-parameter bifurcation point. To validate our analytical findings, the bifurcation curves of fixed points are determined by using MatcontM.

Keywords:

AMSC: 37C25, 37L10, 37M15, 39A30, 92D25

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