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Dynamical analysis of a fractional-order Rosenzweig–MacArthur model incorporating a prey refuge

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  • Moustafa, Mahmoud
  • Mohd, Mohd Hafiz
  • Ismail, Ahmad Izani
  • Abdullah, Farah Aini

Abstract

This paper considers a fractional order Rosenzweig-MacArthur (R-M) model incorporating a prey refuge. The model is constructed and analyzed in detail. The existence, uniqueness, non-negativity and boundedness of the solutions as well as the local and global asymptotic stability of the equilibrium points are studied. Sufficient conditions for the stability and the occurrence of Hopf bifurcation for the fractional order R-M model are demonstrated. The resolution of the paradox of enrichment is investigated. The impact of fractional order and the prey refuge effects on the stability of the system are also studied both theoretically and by using numerical simulations.

Suggested Citation

  • Moustafa, Mahmoud & Mohd, Mohd Hafiz & Ismail, Ahmad Izani & Abdullah, Farah Aini, 2018. "Dynamical analysis of a fractional-order Rosenzweig–MacArthur model incorporating a prey refuge," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 1-13.
    • Handle: RePEc:eee:chsofr:v:109:y:2018:i:c:p:1-13
    DOI: 10.1016/j.chaos.2018.02.008
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    References listed on IDEAS

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