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Mathematical analysis of a fractional-order predator-prey model with prey social behavior and infection developed in predator population

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  • Ghanbari, Behzad
  • Djilali, Salih

Abstract

This manuscript aims to consider a variety of fractional predator-prey models in the presence of an infection developed in the predator population. The crowding behavior plays an essential role in some species surviving, which is a useful strategy for defending the inside group prey. The purpose of considering the fractional-order-derivative is to study the memory effects on the mutual interactions, which has been confirmed to be an intrinsic feature of a dynamic biological system. From the perspective of mathematical results, the local behavior of the equilibrium points, and the existence of Hopf bifurcation are obtained. Besides, the influence of some crucial parameters as memory rate, herd shape, the infection rate in determining the asymptotic behavior of prey and predator are investigated. Further, an efficient numerical technique has been employed to illustrate some illustrative representations for numerical approximation for the solutions. This iterative scheme has been designed using the fundamental theorem of calculus in the fractional sense, and linear polynomial interpolation.

Suggested Citation

  • Ghanbari, Behzad & Djilali, Salih, 2020. "Mathematical analysis of a fractional-order predator-prey model with prey social behavior and infection developed in predator population," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    • Handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920303593
    DOI: 10.1016/j.chaos.2020.109960
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    References listed on IDEAS

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    2. Zulqurnain Sabir & Thongchai Botmart & Muhammad Asif Zahoor Raja & Wajaree Weera, 2022. "An advanced computing scheme for the numerical investigations of an infection-based fractional-order nonlinear prey-predator system," PLOS ONE, Public Library of Science, vol. 17(3), pages 1-13, March.
    3. Zulqurnain Sabir & Juan L. G. Guirao, 2023. "A Soft Computing Scaled Conjugate Gradient Procedure for the Fractional Order Majnun and Layla Romantic Story," Mathematics, MDPI, vol. 11(4), pages 1-14, February.
    4. Bentout, Soufiane & Djilali, Salih & Kumar, Sunil, 2021. "Mathematical analysis of the influence of prey escaping from prey herd on three species fractional predator-prey interaction model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    5. Barman, Dipesh & Roy, Jyotirmoy & Alrabaiah, Hussam & Panja, Prabir & Mondal, Sankar Prasad & Alam, Shariful, 2021. "Impact of predator incited fear and prey refuge in a fractional order prey predator model," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    6. Arjun Hasibuan & Asep Kuswandi Supriatna & Endang Rusyaman & Md. Haider Ali Biswas, 2023. "Harvested Predator–Prey Models Considering Marine Reserve Areas: Systematic Literature Review," Sustainability, MDPI, vol. 15(16), pages 1-23, August.
    7. Belmahi, Naziha & Shawagfeh, Nabil, 2021. "A new mathematical model for the glycolysis phenomenon involving Caputo fractional derivative: Well posedness, stability and bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).

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