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Traveling wavefronts in an anomalous diffusion predator–prey model

  • Asmaa H. Abobakr , Hussien S. Hussien , Mahmoud B. A. Mansour ORCID logo und Hillal M. Elshehabey ORCID logo EMAIL logo
Veröffentlicht/Copyright: 15. Februar 2024
Zeitschrift für Naturforschung A
Aus der Zeitschrift Zeitschrift für Naturforschung A Band 79 Heft 5

Abstract

In this paper, we study traveling wavefronts in an anomalous diffusion predator–prey model with the modified Leslie–Gower and Holling-type II schemes. We perform a traveling wave analysis to show that the model has heteroclinic trajectories connecting two steady state solutions of the resulting system of fractional partial differential equations and corresponding to traveling wavefronts. This also includes numerical results to show the existence of traveling wavefronts. Furthermore, we obtain the numerical time-dependent solutions in order to show the evolution of wavefronts. We find that wavefronts exist that travel faster in the anomalous subdiffusive regime than in the normal diffusive one. Our results emphasize that the main properties of traveling waves and invasions are altered by anomalous subdiffusion in this model.

Keywords: predator–prey model; anomalous diffusion; traveling wavefronts
Corresponding author: Hillal M. Elshehabey, Mathematics Department, South Valley University Faculty of Science, 83523, Qena, Egypt, E-mail:

Acknowledgments

We would like to express our sincere gratitude to the anonymous reviewer for their thoughtful and constructive feedback. Their insightful comments and suggestions have significantly contributed to the improvement of the quality and clarity of this manuscript.

  1. Research ethics: Not applicable.

  2. Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Competing interests: The authors state no competing interests.

  4. Research funding: None declared.

  5. Data availability: Not applicable.

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Received: 2023-11-11
Accepted: 2024-01-13
Published Online: 2024-02-15
Published in Print: 2024-05-27

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/zna-2023-0306
Schlagwörter für diesen Artikel
predator–prey model; anomalous diffusion; traveling wavefronts

Artikel in diesem Heft

  1. Frontmatter
  2. General
  3. Magnetoacoustics and magnetic quantization of Fermi states in relativistic plasmas
  4. Atomic, Molecular & Chemical Physics
  5. Investigations on the EPR parameters and local structures for the substitutional Ti3+ and W5+ centers in stishovite
  6. Dynamical Systems & Nonlinear Phenomena
  7. The effects of viscosity on the structure of shock waves in a van der Waals gas
  8. Traveling wavefronts in an anomalous diffusion predator–prey model
  9. Bifurcation and stability analysis of atherosclerosis disease model characterizing the anti-oxidative activity of HDL during short- and long-time evolution
  10. Nuclear Physics
  11. Investigation of 90,92Zr(n,γ)91,93Zr in the s-process nucleosynthesis
  12. Quantum Theory
  13. Quantum-mechanical treatment of two particles in a potential box
  14. Solid State Physics & Materials Science
  15. Unveiling the luminescence property of Pr-incorporated barium cerate perovskites for white LED applications
  16. Electrical and magnetic properties of MF/CuAl nanocomposites
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