Derivative-order-dependent stability and transient behaviour in a predator–prey system of fractional differential equations. Issue 1 (1st January 2019)

• Record Type: Journal Article
• Authors: Alqahtani, Z. M.; El-Shahed, M.; Mottram, N. J.
• Is Part Of: Letters in biomathematics. Volume 6: Issue 1(2019)
• Page Start: 32
• Page End: 49
• Publication Date: 2019-01-01
• Subjects: Population dynamics -- mathematical modelling -- fractional calculus -- domain of attraction; Biomathematics -- Periodicals; Computational Biology; Biostatistics; Models, Biological; Biomathematics; Periodicals; Periodicals; 570.151
• DOI: 10.1080/23737867.2019.1656115
• Languages: English
• ISSNs: 2373-7867

Abstract

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.