Derivative-order-dependent stability and transient behaviour in a predator–prey system of fractional differential equations
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...
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| Format: | Article |
| Language: | English |
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Intercollegiate Biomathematics Alliance
2019-01-01
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| Series: | Letters in Biomathematics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/23737867.2019.1656115 |
| _version_ | 1819262788715937792 |
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| author | Z. M. Alqahtani M. El-Shahed N. J. Mottram |
| author_facet | Z. M. Alqahtani M. El-Shahed N. J. Mottram |
| author_sort | Z. M. Alqahtani |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-23T20:03:16Z |
| format | Article |
| id | doaj.art-8831f2d235494dd08f19a37a24f004e8 |
| institution | Directory Open Access Journal |
| issn | 2373-7867 |
| language | English |
| last_indexed | 2024-12-23T20:03:16Z |
| publishDate | 2019-01-01 |
| publisher | Intercollegiate Biomathematics Alliance |
| record_format | Article |
| series | Letters in Biomathematics |
| spelling | doaj.art-8831f2d235494dd08f19a37a24f004e82022-12-21T17:33:01ZengIntercollegiate Biomathematics AllianceLetters in Biomathematics2373-78672019-01-0161324910.1080/23737867.2019.16561151656115Derivative-order-dependent stability and transient behaviour in a predator–prey system of fractional differential equationsZ. M. Alqahtani0M. El-Shahed1N. J. Mottram2Princess Nourah Bint Abdulrahman UniversityQassim UniversityUniversity of StrathclydeIn 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.http://dx.doi.org/10.1080/23737867.2019.1656115population dynamicsmathematical modellingfractional calculusdomain of attraction |
| spellingShingle | Z. M. Alqahtani M. El-Shahed N. J. Mottram Derivative-order-dependent stability and transient behaviour in a predator–prey system of fractional differential equations Letters in Biomathematics population dynamics mathematical modelling fractional calculus domain of attraction |
| title | Derivative-order-dependent stability and transient behaviour in a predator–prey system of fractional differential equations |
| title_full | Derivative-order-dependent stability and transient behaviour in a predator–prey system of fractional differential equations |
| title_fullStr | Derivative-order-dependent stability and transient behaviour in a predator–prey system of fractional differential equations |
| title_full_unstemmed | Derivative-order-dependent stability and transient behaviour in a predator–prey system of fractional differential equations |
| title_short | Derivative-order-dependent stability and transient behaviour in a predator–prey system of fractional differential equations |
| title_sort | derivative order dependent stability and transient behaviour in a predator prey system of fractional differential equations |
| topic | population dynamics mathematical modelling fractional calculus domain of attraction |
| url | http://dx.doi.org/10.1080/23737867.2019.1656115 |
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