Qualitative behavior of discrete-time Caputo-Fabrizio logistic model with Allee effect

Karakaya H., KARTAL Ş., oeztuerk I.

INTERNATIONAL JOURNAL OF BIOMATHEMATICS, cilt.17, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1142/s1793524523500390
  • Dergi Adı: INTERNATIONAL JOURNAL OF BIOMATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, BIOSIS, zbMATH
  • Anahtar Kelimeler: Caputo-Fabrizio fractional derivative, two-step Adams-Basforth method, logistic differential equation, Neimark-Sacker bifurcation, Allee effect
  • Erciyes Üniversitesi Adresli: Evet

Özet

The aim of this paper is to investigate the dynamic behaviors of fractional- order logistic model with Allee effects in Caputo-Fabrizio sense. First of all, we apply the two-step Adams-Bashforth scheme to discretize the fractional-order logistic differential equation and obtain the two-dimensional discrete system. The parametric conditions for local asymptotic stability of equilibrium points are obtained by Schur-Chon criterion. Moreover, we discuss the existence and direction for Neimark-Sacker bifurcations with the help of center manifold theorem and bifurcation theory. Numerical simulations are provided to illustrate theoretical discussion. It is observed that Allee effect plays an important role in stability analysis. Strong Allee effect in population enhances the stability of the coexisting steady state. In additional, the effect of fractional-order derivative on dynamic behavior of the system is also investigated.