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Dynamic analysis of fractional-order singular Holling type-II predator–prey system

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  • Nosrati, Komeil
  • Shafiee, Masoud

Abstract

In this paper, a fractional-order singular (FOS) predator–prey model with Holling type-II functional response has been introduced, and the mathematical behavior of the model from the aspect of local stability is investigated. Through the fractional calculus and economic theory, a new and more realistic predator–prey model has been extended, and the solvability condition is presented. Besides, numerical simulations are considered to illustrate the effectiveness of the numerical method and confirm the theoretical results to explore the impacts of fractional-order and economic interest on the presented system in biological context. It is found that the presence of fractional-order in the differential model can improve the stability of the solutions and enrich the dynamics of system. In addition, singular models exhibit more complicated dynamics rather than standard models, especially the bifurcation phenomena, which can reveal the instability mechanism of systems.

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  • 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.
    • Handle: RePEc:eee:apmaco:v:313:y:2017:i:c:p:159-179
    DOI: 10.1016/j.amc.2017.05.067
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    References listed on IDEAS

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    1. Zhang, Yue & Zhang, Qingling & Yan, Xing-Gang, 2014. "Complex dynamics in a singular Leslie–Gower predator–prey bioeconomic model with time delay and stochastic fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 180-191.
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    5. H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Journal of Political Economy, University of Chicago Press, vol. 62(2), pages 124-124.
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    Cited by:

    1. Yousef, Fatma Bozkurt & Yousef, Ali & Maji, Chandan, 2021. "Effects of fear in a fractional-order predator-prey system with predator density-dependent prey mortality," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. Nosrati, Komeil & Belikov, Juri & Tepljakov, Aleksei & Petlenkov, Eduard, 2023. "Extended fractional singular kalman filter," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    3. Nosrati, Komeil & Shafiee, Masoud, 2018. "Fractional-order singular logistic map: Stability, bifurcation and chaos analysis," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 224-238.
    4. 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.
    5. Ghosh, Uttam & Pal, Swadesh & Banerjee, Malay, 2021. "Memory effect on Bazykin’s prey-predator model: Stability and bifurcation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    6. Huang, Chengdai & Liu, Heng & Chen, Xiaoping & Cao, Jinde & Alsaedi, Ahmed, 2020. "Extended feedback and simulation strategies for a delayed fractional-order control system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    7. Zhang, Xuefeng & Zhao, Zeli, 2020. "Robust stabilization for rectangular descriptor fractional order interval systems with order 0 < α < 1," Applied Mathematics and Computation, Elsevier, vol. 366(C).

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