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Journals / Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2022 / Cilt: 15 - Sayı: 3

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

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

Deniz ELMACI
Figen KANGALGİL
Pages
775–787
Publication Date
2022-12-30
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Following that, the model's bifurcation diagram and the triangle-shaped stability zone are provided.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, the dynamical behaviors of a prey–predator model with multiple strong Allee effect are investigated.
📊
Key Findings & Data: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.
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Conclusion & Impact:Following that, the model's bifurcation diagram and the triangle-shaped stability zone are provided.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Prey-predator model · strong Allee effect · Neimark-Sacker bifurcation analysis

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.

Özet

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.

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Cite This Article

ELMACI, D., KANGALGİL, F. (2022). Stability, Neimark-Sacker Bifurcation Analysis of a Prey-Predator Model with Strong Allee Effect and Chaos Control. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 15 - Sayı: 3, 775–787. https://ajindex.com/articles/859230

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