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Complex Dynamic Behaviour of Food Web Model with Generalized Fractional Operator

Author

Listed:
  • Ajay Kumar

    (Department of Mathematics, National Institute of Technology, Jamshedpur 831014, Jharkhand, India)

  • Sara Salem Alzaid

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 1142, Riyadh 11989, Saudi Arabia)

  • Badr Saad T. Alkahtani

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 1142, Riyadh 11989, Saudi Arabia)

  • Sunil Kumar

    (Department of Mathematics, National Institute of Technology, Jamshedpur 831014, Jharkhand, India
    Department of Mathematics, College of Science, King Saud University, P.O. Box 1142, Riyadh 11989, Saudi Arabia
    Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman P.O. Box 346, United Arab Emirates
    Department of Mathematics, University Centre for Research and Development, Chandigarh University, Gharuan, Mohali 140413, Punjab, India)

Abstract

We apply a new generalized Caputo operator to investigate the dynamical behaviour of the non-integer food web model (FWM). This dynamical model has three population species and is nonlinear. Three types of species are considered in this population: prey species, intermediate predators, and top predators, and the top predators are also divided into mature and immature predators. We calculated the uniqueness and existence of the solutions applying the fixed-point hypothesis. Our study examines the possibility of obtaining new dynamical phase portraits with the new generalized Caputo operator and demonstrates the portraits for several values of fractional order. A generalized predictor–corrector (P-C) approach is utilized in numerically solving this food web model. In the case of the nonlinear equations system, the effectiveness of the used scheme is highly evident and easy to implement. In addition, stability analysis was conducted for this numerical scheme.

Suggested Citation

  • Ajay Kumar & Sara Salem Alzaid & Badr Saad T. Alkahtani & Sunil Kumar, 2022. "Complex Dynamic Behaviour of Food Web Model with Generalized Fractional Operator," Mathematics, MDPI, vol. 10(10), pages 1-23, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1702-:d:816544
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    References listed on IDEAS

    as
    1. Erturk, Vedat Suat & Kumar, Pushpendra, 2020. "Solution of a COVID-19 model via new generalized Caputo-type fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Kumar, Ajay & Kumar, Sunil, 2022. "A study on eco-epidemiological model with fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. Kumar, Sunil & Kumar, Ajay & Samet, Bessem & Gómez-Aguilar, J.F. & Osman, M.S., 2020. "A chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatment," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    4. Khan, Aziz & Abdeljawad, Thabet & Gómez-Aguilar, J.F. & Khan, Hasib, 2020. "Dynamical study of fractional order mutualism parasitism food web module," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
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    Cited by:

    1. A. E. Matouk & T. N. Abdelhameed & D. K. Almutairi & M. A. Abdelkawy & M. A. E. Herzallah, 2023. "Existence of Self-Excited and Hidden Attractors in the Modified Autonomous Van Der Pol-Duffing Systems," Mathematics, MDPI, vol. 11(3), pages 1-13, January.

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