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Journals / Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2022 / Cilt: 15 - Sayı: 1

Stability and Period-Doubling Bifurcation in a Modified Commensal Symbiosis Model with Allee Effect

Seval IŞIK
Pages
310–324
Publication Date
2022-03-27
DOI
—
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AI Summary & Key Takeaways

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

More specifically, when the parameter 𝛿 is choosen as a bifurcation parameter, it is seen that the considered discrete-time commensal symbiosis model shows very rich nonlinear dynamical.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this article, the qualitative behaviour of discrete-time commensal symbiosis model which is obtained by implementing the forward Euler’s scheme is discussed in detail.
📊
Key Findings & Data:Firstly, the local stability conditions of fixed points of the model are studied.
💡
Conclusion & Impact:More specifically, when the parameter 𝛿 is choosen as a bifurcation parameter, it is seen that the considered discrete-time commensal symbiosis model shows very rich nonlinear dynamical.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Allee effect · stability · Period-Doubling bifurcation

Abstract

In this article, the qualitative behaviour of discrete-time commensal symbiosis model which is obtained by implementing the forward Euler’s scheme is discussed in detail. Firstly, the local stability conditions of fixed points of the model are studied. It is proved that the considered model undergoes Period-Doubling bifurcation around coexistence fixed point with the help of bifurcation theory. In order to support the accuracy of obtained analytical finding, some parameter values have been determined and numerical simulations are carried out for these parameter values. Numerical simulations display new and rich nonlinear dynamical behaviours. More specifically, when the parameter 𝛿 is choosen as a bifurcation parameter, it is seen that the considered discrete-time commensal symbiosis model shows very rich nonlinear dynamical.

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Cite This Article

IŞIK, S. (2022). Stability and Period-Doubling Bifurcation in a Modified Commensal Symbiosis Model with Allee Effect. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 15 - Sayı: 1, 310–324. https://ajindex.com/articles/395436

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References (6)

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