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

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

Chaos, Solitons & Fractals, 2023, vol. 175, issue P1

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.

Keywords: Prey-predator model; Caputo fractional derivative; Period-doubling(PD) and Neimark–Sacker (NS) bifurcations; Harvesting; 0-1 chaos test; Chaos control (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923008330

DOI: 10.1016/j.chaos.2023.113932

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