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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2023 / Cilt: 52 Sayı: 4

Bifurcation analysis and chaos control of a discrete-time prey-predator model with Allee effect

Özlem AK GÜMÜŞ
Sayfa
1029–1045
Yayın Tarihi
2023-08-15
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Numerical simulations are performed to support the theoretical results.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this study, a discrete-time prey-predator model based on the Allee effect is presented.
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Temel Bulgular & Veri:We examine the parametric conditions for the local asymptotic stability of the fixed points of this model.
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Sonuç & Katkı:Numerical simulations are performed to support the theoretical results.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:prey-predator model · fixed point · stability

Abstract

In this study, a discrete-time prey-predator model based on the Allee effect is presented. We examine the parametric conditions for the local asymptotic stability of the fixed points of this model. Furthermore, with the use of the center manifold theorem and bifurcation theory, we analyze the existence and directions of period-doubling and Neimark-Sacker bifurcations. The plots of maximum Lyapunov exponents provide indications of complexity and chaotic behavior. The feedback control approach is presented to stabilize the unstable fixed point. Numerical simulations are performed to support the theoretical results.

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Bu Makaleye Atıf Yap

GÜMÜŞ, Ö. A. (2023). Bifurcation analysis and chaos control of a discrete-time prey-predator model with Allee effect. Hacettepe Journal of Mathematics and Statistics, Cilt: 52 Sayı: 4, 1029–1045. https://ajindex.com/articles/958701

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Kaynakça (18)

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