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Analysis and pattern formation scenarios in the superdiffusive system of predation described with Caputo operator

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  • Owolabi, Kolade M.
  • Pindza, Edson
  • Atangana, Abdon

Abstract

The concept of a fractional derivative is introduced to the predator-prey system to describe the species anomalous superdiffusive process. To achieve this, a new class of predator-prey model with the Beddington-DeAngelis functional response is formulated in the sense of the Caputo fractional order operator. This work aims to give a mathematical basis for computational studies of a two-variable fractional reaction-diffusion system in one and two dimensions from biological and numerical perspectives. As a result, some details of the local and global dynamics of the reaction-diffusion system are provided by using the idea of the linear stability analysis and well-known dynamical systems theory to derive conditions on the parameters which can guarantee biologically meaningful equilibria also serve as a guide in ensuring the correct choice of parameters when numerically experimenting with the solutions of the full fractional reaction-diffusion model. The behavior of the new dynamical system is examined for both diffusive and non-diffusive systems at different instances of fractional order.

Suggested Citation

  • Owolabi, Kolade M. & Pindza, Edson & Atangana, Abdon, 2021. "Analysis and pattern formation scenarios in the superdiffusive system of predation described with Caputo operator," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921008225
    DOI: 10.1016/j.chaos.2021.111468
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    References listed on IDEAS

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    1. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Mathematical modeling for the impacts of deforestation on wildlife species using Caputo differential operator," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 32-40.
    2. Owolabi, Kolade M. & Karaagac, Berat, 2020. "Chaotic and spatiotemporal oscillations in fractional reaction-diffusion system," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
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    1. Izadi, Mohammad & Yüzbaşı, Şuayip & Adel, Waleed, 2022. "Accurate and efficient matrix techniques for solving the fractional Lotka–Volterra population model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    2. Alqhtani, Manal & Owolabi, Kolade M. & Saad, Khaled M., 2022. "Spatiotemporal (target) patterns in sub-diffusive predator-prey system with the Caputo operator," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    3. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Shoaib, Muhammad & Kiani, Adiqa Kausar, 2022. "Fractional order Lorenz based physics informed SARFIMA-NARX model to monitor and mitigate megacities air pollution," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    4. Troparevsky, M.I. & Muszkats, J.P. & Seminara, S.A. & Zitto, M.E. & Piotrkowski, R., 2022. "Modeling particulate pollutants dispersed in the atmosphere using fractional turbulent diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    5. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Rafiq, Naila & Shoaib, Muhammad & Kiani, Adiqa Kausar & Shu, Chi-Min, 2022. "Design of intelligent computing networks for nonlinear chaotic fractional Rossler system," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    6. Alqhtani, Manal & Owolabi, Kolade M. & Saad, Khaled M. & Pindza, Edson, 2022. "Efficient numerical techniques for computing the Riesz fractional-order reaction-diffusion models arising in biology," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).

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