Analyzing bifurcation, stability, and chaos control for a discrete-time prey-predator model with Allee effect
TURKISH JOURNAL OF MATHEMATICS, cilt.46, sa.6, ss.2047-2068, 2022 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 46 Sayı: 6
- Basım Tarihi: 2022
- Doi Numarası: 10.55730/1300-0098.3253
- Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.2047-2068
- Sivas Cumhuriyet Üniversitesi Adresli: Evet
Özet
In this paper, the qualitative behavior of a discrete-time prey-predator model with Allee effect in prey
population is discussed. Firstly, the existence of the fixed points and their topological classification are analyzed
algebraically. Then, the conditions of existence for both period-doubling and Neimark–Sacker bifurcations arising from
coexistence fixed point with the help of the center manifold theorem and bifurcation theory are investigated. OGY
feedback control method is implemented to control chaos in the proposed model due to the emergence of bifurcations.
Finally, numerical simulations are performed to support the theoretical findings.