Qualitative Analysis and Hopf Bifurcation for a Fractional-Order Ratio-Dependent Prey–Predator Model

Celik C., Degerli K.

International Conference on Fractional Calculus and Applications, ICFCA 2024, Sousse, Tunus, 26 - 30 Aralık 2024, cilt.505, ss.145-154, (Tam Metin Bildiri) identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 505
  • Doi Numarası: 10.1007/978-3-031-95381-1_8
  • Basıldığı Şehir: Sousse
  • Basıldığı Ülke: Tunus
  • Sayfa Sayıları: ss.145-154
  • Anahtar Kelimeler: Fractional-order, Global stability, Hopf bifurcation, Lyapunov function, Numerical simulation, Predator–prey model, Time delay
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this chapter, a fractional order ratio-dependent predator–prey system with time delay, where the dynamics is logistic with the carrying capacity proportional to prey population, is studied. Mainly, a Hopf bifurcation parameter is taken as the time delay, the local stability of a positive equilibrium and the presence of Hopf bifurcations are determined. Moreover, by defining Lyapunov function for this system, global stability of the solution are proven. Finally, to support our new theoretical results, two different numerical examples are illustrated, choosing two different fractional orders q.