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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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    1. Garrappa, Roberto, 2015. "Trapezoidal methods for fractional differential equations: Theoretical and computational aspects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 110(C), pages 96-112.
    2. Ivanov, Tihomir & Dimitrova, Neli, 2017. "A predator–prey model with generic birth and death rates for the predator and Beddington–DeAngelis functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 133(C), pages 111-123.
    3. Ji, Guilin & Ge, Qing & Xu, Jiabo, 2016. "Dynamic behaviors of a fractional order two-species cooperative systems with harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 51-55.
    4. Sung Kyu Choi & Bowon Kang & Namjip Koo, 2014. "Stability for Caputo Fractional Differential Systems," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, January.
    5. Nosrati, Komeil & Shafiee, Masoud, 2017. "Dynamic analysis of fractional-order singular Holling type-II predator–prey system," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 159-179.
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    Cited by:

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