On the qualitative study of a discrete fractional order prey–predator model with the effects of harvesting on predator population

Uddin M. J., Rana S. M. S., IŞIK S., KANGALGİL F.

Chaos, Solitons and Fractals, cilt.175, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 175
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1016/j.chaos.2023.113932
  • Dergi Adı: Chaos, Solitons and Fractals
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Compendex, INSPEC, zbMATH
  • Anahtar Kelimeler: 0-1 chaos test, Caputo fractional derivative, Chaos control, Harvesting, Period-doubling(PD) and Neimark–Sacker (NS) bifurcations, Prey-predator model
  • Sivas Cumhuriyet Üniversitesi Adresli: Evet

Özet

This research investigates the discrete prey–predator model by including harvesting on the predator population, in the sense of Caputo fractional derivative. We define the topological categories of the model fixed points. We demonstrate mathematically that, under certain parametric conditions, a fractional order prey-predator model undergoes both a Neimark–Sacker (NS) and a Period-doubling (PD) bifurcations. Using the central manifold and bifurcation theory, we present proof for NS and PD bifurcations. It has been discovered that the fractional order prey-predator model's dynamical behavior is significantly influenced by the parameter values and the initial conditions. Two chaos control techniques have been used to eliminate the chaos in the model. In order to support our theoretical and analytical results and to illustrate complex and chaotic behavior, numerical simulations have been shown.