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

Alqahtani, Z.M., El-Shahed, M. and Mottram, N.J. (2019) Derivative-order-dependent stability and transient behaviour in a predator–prey system of fractional differential equations. Letters in Biomathematics, 6(1), pp. 32-49. (doi: 10.1080/23737867.2019.1656115)

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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.

Item Type:Articles
Additional Information:One of the authors (N.J.M.) was partially supported by the United Kingdom Medical Research Council (MRC) via grant no. G0902331.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Mottram, Professor Nigel
Authors: Alqahtani, Z.M., El-Shahed, M., and Mottram, N.J.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Letters in Biomathematics
Publisher:Taylor & Francis
ISSN:2373-7867
ISSN (Online):2373-7867
Published Online:11 December 2019
Copyright Holders:Copyright © 2019 The Authors
First Published:First published in Letters in Biomathematics 6(1): 32-49
Publisher Policy:Reproduced under a Creative Commons License

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