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

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  • Uddin, Md. Jasim
  • Rana, Sarker Md. Sohel
  • Işık, Seval
  • Kangalgil, Figen

Abstract

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.

Suggested Citation

  • Uddin, Md. Jasim & Rana, Sarker Md. Sohel & Işık, Seval & Kangalgil, Figen, 2023. "On the qualitative study of a discrete fractional order prey–predator model with the effects of harvesting on predator population," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923008330
    DOI: 10.1016/j.chaos.2023.113932
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    References listed on IDEAS

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    1. Salman, S.M. & Yousef, A.M. & Elsadany, A.A., 2016. "Stability, bifurcation analysis and chaos control of a discrete predator-prey system with square root functional response," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 20-31.
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    6. Pati, N.C. & Layek, G.C. & Pal, Nikhil, 2020. "Bifurcations and organized structures in a predator-prey model with hunting cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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