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, Tunisia, 26 - 30 December 2024, vol.505, pp.145-154, (Full Text) identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 505
  • Doi Number: 10.1007/978-3-031-95381-1_8
  • City: Sousse
  • Country: Tunisia
  • Page Numbers: pp.145-154
  • Keywords: Fractional-order, Global stability, Hopf bifurcation, Lyapunov function, Numerical simulation, Predator–prey model, Time delay
  • Yıldız Technical University Affiliated: Yes

Abstract

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.