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A fractal–fractional-order modified Predator–Prey mathematical model with immigrations

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  • Ali, Zeeshan
  • Rabiei, Faranak
  • Hosseini, Kamyar

Abstract

This manuscript aims to study a modified predator–prey model’s existence, stability, and dynamics under the newly developed fractal–fractional order operator in the Caputo–Fabrizio sense. The existence theory of the proposed model carries out through the Leray–Schauder alternative and sufficient conditions for stability are established using the classical technique of nonlinear functional analysis. The numerical results are obtained by the fractal–fractional Adam–Bashforth method in the Caputo–Fabrizio sense. The numerical results show that small immigrations invoke stable convergence in the predator–prey ecosystem. This means that a small number of sporadic immigrants can stabilize natural predator–prey populations.

Suggested Citation

  • Ali, Zeeshan & Rabiei, Faranak & Hosseini, Kamyar, 2023. "A fractal–fractional-order modified Predator–Prey mathematical model with immigrations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 466-481.
    • Handle: RePEc:eee:matcom:v:207:y:2023:i:c:p:466-481
    DOI: 10.1016/j.matcom.2023.01.006
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    References listed on IDEAS

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    Cited by:

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    5. Kanwal, Tanzeela & Hussain, Azhar & Avcı, İbrahim & Etemad, Sina & Rezapour, Shahram & Torres, Delfim F.M., 2024. "Dynamics of a model of polluted lakes via fractal–fractional operators with two different numerical algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
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    7. Avcı, İbrahim & Lort, Hüseyin & Tatlıcıoğlu, Buğce E., 2023. "Numerical investigation and deep learning approach for fractal–fractional order dynamics of Hopfield neural network model," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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