On the analysis of stability, bifurcation, and chaos control of discrete-time predator-prey model with Allee effect on predator

IŞIK S., KANGALGİL F.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.51, sa.2, ss.404-420, 2022 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 51 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.15672/hujms.728889
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.404-420
  • Anahtar Kelimeler: predator-prey model, fixed point, stability, Neimark-Sacker bifurcation, Allee effect, OGY control method, NEIMARK-SACKER BIFURCATION, BEHAVIOR, SYSTEMS
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

In this paper, a discrete predator-prey model with Allee effect which is obtained by the forward Euler method has been investigated. The local stability conditions of the model at the fixed point have been discussed. In addition, it is shown that the model undergoes Neimark-Sacker bifurcation by using bifurcation theory. Then, the direction of Neimark-Sacker bifurcation has been given. The OGY method is applied in order to control chaos in considered model due to emergence of Neimark-Sacker bifurcation. Some numerical simulations such as phase portraits and bifurcation figures have been presented to support the theoretical results. Also, the chaotic features are justified numerically by computing Lyapunov exponents. Because of consistency with the biological facts, the parameter values have been taken from literature [Controlling chaos and Neimark-Sacker bifurcation discrete-time predator-prey system, Hacet. J. Math. Stat. 49 (5), 1761-1776, 2020].