Affiliation:
1. DOKUZ EYLUL UNIVERSITY, BERGAMA VOCATIONAL SCHOOL
2. Dokuz Eylül University Bergama Vocational School
Abstract
In this study, the dynamical behaviors of a prey–predator model with multiple strong Allee effect are investigated. The fixed points of the model are examined for existence and topological classification. By selecting as the bifurcation parameter $\beta$, it is demonstrated that the model can experience a Neimark-Sacker bifurcation at the unique positive fixed point. Bifurcation theory is used to present the Neimark-Sacker bifurcation conditions of existence and the direction of the bifurcation. Additionally, some numerical simulations are provided to back up the analytical result. Following that, the model's bifurcation diagram and the triangle-shaped stability zone are provided.
Publisher
Erzincan Universitesi Fen Bilimleri Ensitusu Dergisi
Reference26 articles.
1. [1] Arancibia-Ibarra, C., (2019), The basins of attraction in a modified May–Holling–Tanner predator–
prey model with Allee affect, Nonlinear Analysis, 185, 15-28.
2. [2] Kundu, S., Maitra, S., (2019), Asymptotic behaviors of a two prey one predator model with cooperation
among the prey species in a stochastic environment, Journal of Applied Mathematics and
Computing, 61(1), 505-531.
3. [3] Martinez-Jeraldo, N., Aguirre, P., (2019), Allee effect acting on the prey species in a Leslie–Gower
predation model, Nonlinear Analysis: Real World Applications, 45, 895-917.
4. [4] Elaydi, S., (1996), An introduction to difference equations, Springer-Verlag, New York, 10, 978-1.
5. [5] Kuznetsov, Y. A., Kuznetsov, I. A., Kuznetsov, Y, (1998), Elements of applied bifurcation theory
(Vol. 112, pp. xx+-591), New York: Springer.