Periodic Solutions of a System of Delay Differential Equations for a Small Delay
We prove the existence of an asymptotically stable periodic solution of a system of delay differential equations with a small time delay t > 0. To achieve this, we transform the system of equations into a system of perturbed ordinary differential equations and then use perturbation results to sho...
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| Format: | Article |
| Language: | English |
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Sultan Qaboos University
2002-06-01
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| Series: | Sultan Qaboos University Journal for Science |
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| Online Access: | https://journals.squ.edu.om/index.php/squjs/article/view/298 |
| _version_ | 1818881961294299136 |
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| author | Adu A.M. Wasike Wandera Ogana |
| author_facet | Adu A.M. Wasike Wandera Ogana |
| author_sort | Adu A.M. Wasike |
| collection | DOAJ |
| description | We prove the existence of an asymptotically stable periodic solution of a system of delay differential equations with a small time delay t > 0. To achieve this, we transform the system of equations into a system of perturbed ordinary differential equations and then use perturbation results to show the existence of an asymptotically stable periodic solution. This approach is contingent on the fact that the system of equations with t = 0 has a stable limit cycle. We also provide a comparative study of the solutions of the original system and the perturbed system. This comparison lays the ground for proving the existence of periodic solutions of the original system by Schauder's fixed point theorem. |
| first_indexed | 2024-12-19T15:10:11Z |
| format | Article |
| id | doaj.art-177571f1fac2418ba5f4039bbd80d07b |
| institution | Directory Open Access Journal |
| issn | 1027-524X 2414-536X |
| language | English |
| last_indexed | 2024-12-19T15:10:11Z |
| publishDate | 2002-06-01 |
| publisher | Sultan Qaboos University |
| record_format | Article |
| series | Sultan Qaboos University Journal for Science |
| spelling | doaj.art-177571f1fac2418ba5f4039bbd80d07b2022-12-21T20:16:20ZengSultan Qaboos UniversitySultan Qaboos University Journal for Science1027-524X2414-536X2002-06-017229530210.24200/squjs.vol7iss2pp295-302297Periodic Solutions of a System of Delay Differential Equations for a Small DelayAdu A.M. Wasike0Wandera Ogana1Department of Mathematics, University of Nairobi, P.O.Box 30197, Nairobi KenyaDepartment of Mathematics, University of Nairobi, P.O.Box 30197, Nairobi KenyaWe prove the existence of an asymptotically stable periodic solution of a system of delay differential equations with a small time delay t > 0. To achieve this, we transform the system of equations into a system of perturbed ordinary differential equations and then use perturbation results to show the existence of an asymptotically stable periodic solution. This approach is contingent on the fact that the system of equations with t = 0 has a stable limit cycle. We also provide a comparative study of the solutions of the original system and the perturbed system. This comparison lays the ground for proving the existence of periodic solutions of the original system by Schauder's fixed point theorem.https://journals.squ.edu.om/index.php/squjs/article/view/298Periodic Solutions, Delay Differential Equations, Schauder’s Fixed Point Theorem. |
| spellingShingle | Adu A.M. Wasike Wandera Ogana Periodic Solutions of a System of Delay Differential Equations for a Small Delay Sultan Qaboos University Journal for Science Periodic Solutions, Delay Differential Equations, Schauder’s Fixed Point Theorem. |
| title | Periodic Solutions of a System of Delay Differential Equations for a Small Delay |
| title_full | Periodic Solutions of a System of Delay Differential Equations for a Small Delay |
| title_fullStr | Periodic Solutions of a System of Delay Differential Equations for a Small Delay |
| title_full_unstemmed | Periodic Solutions of a System of Delay Differential Equations for a Small Delay |
| title_short | Periodic Solutions of a System of Delay Differential Equations for a Small Delay |
| title_sort | periodic solutions of a system of delay differential equations for a small delay |
| topic | Periodic Solutions, Delay Differential Equations, Schauder’s Fixed Point Theorem. |
| url | https://journals.squ.edu.om/index.php/squjs/article/view/298 |
| work_keys_str_mv | AT aduamwasike periodicsolutionsofasystemofdelaydifferentialequationsforasmalldelay AT wanderaogana periodicsolutionsofasystemofdelaydifferentialequationsforasmalldelay |