Stability analysis of a continuous model of mutualism with delay dynamics
| dc.contributor.author | Roberts, Jason A. | * |
| dc.contributor.author | Joharjee, Najwa G. | * |
| dc.date.accessioned | 2016-05-17T08:58:37Z | |
| dc.date.available | 2016-05-17T08:58:37Z | |
| dc.date.issued | 2016-05-31 | |
| dc.identifier.citation | Roberts, J. A., & Joharjee, N. G. (2016). Stability analysis of a continuous model of mutualism with delay dynamics. International Mathematical Forum, 11(10), 463-473. http://dx.doi.org/10.12988/imf.2016.616 | en |
| dc.identifier.doi | 10.12988/imf.2016.616 | |
| dc.identifier.uri | http://hdl.handle.net/10034/609519 | |
| dc.description.abstract | In this paper we introduce delay dynamics to a coupled system of ordinary differential equations which represent two interacting species exhibiting facultative mutualistic behaviour. The delays are represen- tative of the beneficial effects of the indirect, interspecies interactions not being realised immediately. We show that the system with delay possesses a continuous solution, which is unique. Furthermore we show that, for suitably-behaved, positive initial functions that this unique solution is bounded and remains positive, i.e. both of the components representing the two species remain greater than zero. We show that the system has a positive equilibrium point and prove that this point is asymptotically stable for positive solutions and that this stability property is not conditional upon the delays. | |
| dc.language.iso | en | en |
| dc.publisher | Hikari | en |
| dc.relation.url | http://www.m-hikari.com/imf.html | en |
| dc.rights | An error occurred on the license name. | * |
| dc.rights.uri | An error occurred getting the license - uri. | en |
| dc.subject | Delay differential equations | en |
| dc.subject | Stability | en |
| dc.subject | Mathematical Ecology | en |
| dc.title | Stability analysis of a continuous model of mutualism with delay dynamics | en |
| dc.type | Article | en |
| dc.identifier.eissn | 1312-7594 | |
| dc.contributor.department | University of Chester; King Abdul Aziz University | en |
| dc.identifier.journal | International Mathematical Forum | |
| dc.date.accepted | 2016-04-29 | |
| or.grant.openaccess | Yes | en |
| rioxxterms.funder | Unfunded | en |
| rioxxterms.identifier.project | Unfunded | en |
| rioxxterms.version | AM | en |
| rioxxterms.licenseref.startdate | 2016-05-17 | |
| html.description.abstract | In this paper we introduce delay dynamics to a coupled system of ordinary differential equations which represent two interacting species exhibiting facultative mutualistic behaviour. The delays are represen- tative of the beneficial effects of the indirect, interspecies interactions not being realised immediately. We show that the system with delay possesses a continuous solution, which is unique. Furthermore we show that, for suitably-behaved, positive initial functions that this unique solution is bounded and remains positive, i.e. both of the components representing the two species remain greater than zero. We show that the system has a positive equilibrium point and prove that this point is asymptotically stable for positive solutions and that this stability property is not conditional upon the delays. |
