Derivative-order-dependent stability and transient behaviour in a predator–prey system of fractional differential equations

Authors

  • Z. M. Alqahtani Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia ORCID: http://orcid.org/0000-0002-6726-6597 Author
  • M. El- Shahed Department of Mathematics, Faculty of Art and Sciences, Qassim University, Unizah, Saudi Arabia ORCID: http://orcid.org/0000-0001-9508-3192 Author
  • N. J. Mottram Department of Mathematics & Statistics, University of Strathclyde, Glasgow, UK ORCID: http://orcid.org/0000-0002-7265-0059 Author

DOI:

https://doi.org/10.30707/LiB6.2Alqahtani

Keywords:

Population dynamics, Mathematical modelling, Fractional calculus, Domain of attraction

Abstract

In this paper, the static and dynamic behaviour of a fractional-order predator–prey model are studied, where the nonlinear interactions between the two species lead to multiple stable states. As has been found in many previous systems, the stability of such states can be dependent on the fractional order of the time derivative, which is included as a phenomenological model of memory-effects in the predator and prey species. However, what is less well understood is the transient behaviour and dependence of the observed domains of attraction for each stable state on the order of the fractional time derivative. These dependencies are investigated using analytical (for the stability of equilibria) and numerical (for the observed domains of attraction) techniques. Results reveal far richer dynamics compared to the integer-order model. We conclude that, as well as the species and controllable parameters, the memory effect of the species will play a role in the observed behaviour of the system.

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Published

2023-11-22

How to Cite

Derivative-order-dependent stability and transient behaviour in a predator–prey system of fractional differential equations. (2023). Letters in Biomathematics, 6(2), 32-49. https://doi.org/10.30707/LiB6.2Alqahtani

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