Güçlü Allee Etkili Av-Avcı Modelinin Kararlılığı, Neimark-Sacker Çatallanma Analizi ve Kaos Kontrol

Year 2022, , 775 - 787, 30.12.2022

Deniz Elmacı , Figen Kangalgil

https://doi.org/10.18185/erzifbed.1207680

Abstract

Bu çalışmada, çoklu güçlü Allee etkisi içeren bir av-avcı modelinin dinamik davranışları araştırılmıştır. Modelin sabit noktalarının varlığı ve topolojik sınıflandırması incelenmiştir. $\beta$ çatallanma parametresi olarak seçildiğinde, modelin benzersiz pozitif sabit noktada bir Neimark-Sacker çatallanması olacağı gösterilmiştir. Çatallanma teorisi, Neimark-Sacker çatallanma varoluş koşullarını ve çatallanmanın yönünü sunmak için kullanılır. Ek olarak, bazı sayısal simülasyonlar, analitik sonucu desteklemek için sunulmuştur. Bunu takiben, modelin çatallanma diyagramı ve üçgen şeklindeki kararlılık bölgesi verilmiştir.

Keywords

Prey-predator model, strong Allee effect, Neimark-Sacker bifurcation analysis

Stability, Neimark-Sacker Bifurcation Analysis of a Prey-Predator Model with Strong Allee Effect and Chaos Control

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.

Keywords

Prey-predator model, strong Allee effect, Neimark-Sacker bifurcation analysis

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