An Investigation of the Discrete-Time Model Subject to Immigration, Harvesting, and Allee Effect

Işlk S., KANGALGİL F., Uddin M. J., Rana S. M. S.

International Journal of Bifurcation and Chaos, cilt.35, sa.2, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 35 Sayı: 2
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1142/s0218127425500221
  • Dergi Adı: International Journal of Bifurcation and Chaos
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Allee effect, bifurcation, harvesting, immigration, Predator-prey model, stability
  • Sivas Cumhuriyet Üniversitesi Adresli: Evet

Özet

This paper deals with the dynamic behaviors of a discrete-time fractional-order predator-prey model in the presence of both the Allee effect and immigration on the prey population and in the presence of harvesting on the predator population. The existence and uniqueness and parametric conditions for local asymptotic stability of fixed points of the discrete-time fractional-order model are studied. Moreover, using the center manifold theorem and bifurcation theory, it is shown that the considered model undergoes flip and Neimark-Sacker bifurcations in a small neighborhood of the interior fixed point. Then, the direction of bifurcation is calculated. A feedback controller is implemented in the proposed model to control chaos thanks to the emergence of the Neimark-Sacker bifurcation. Furthermore, numerical analysis confirms the theoretical analysis with the help of Matlab software.