Neimark-Sacker bifurcation and stability analysis of a discrete-time prey-predator model with Allee effect in prey

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Kangalgil F.

ADVANCES IN DIFFERENCE EQUATIONS, 2019 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1186/s13662-019-2039-y
  • Dergi Adı: ADVANCES IN DIFFERENCE EQUATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Allee effect, Prey-predator model, Stability, 39A28, 39A30, 92B05, CHAOS CONTROL, DYNAMICS, DENSITY
  • Dokuz Eylül Üniversitesi Adresli: Hayır

Özet

In this paper, the dynamical behaviors of a discrete-time prey-predator model with Allee effect on the prey population are investigated. The existence and topological classification of the fixed points of the model are analyzed. It is shown that the model can undergo a Neimark-Sacker bifurcation at the unique positive fixed point by choosing a as a bifurcation parameter. The conditions of the existence for Neimark-Sacker bifurcation and the direction of bifurcation via bifurcation theory are presented. Also, some numerical simulations are presented to support of the analytical finding. Then bifurcation diagrams and phase portraits of the model are given.