Periodic Solutions of a System of Delay Differential Equations for a Small Delay

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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Main Authors: Adu A.M. Wasike, Wandera Ogana
Format: Article
Language:English
Published: Sultan Qaboos University 2002-06-01
Series:Sultan Qaboos University Journal for Science
Subjects:
Periodic Solutions, Delay Differential Equations, Schauder’s Fixed Point Theorem.
Online Access:https://journals.squ.edu.om/index.php/squjs/article/view/298
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spelling doaj-177571f1fac2418ba5f4039bbd80d07b2020-11-25T01:08:14ZengSultan 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.
collection DOAJ
language English
format Article
sources DOAJ
author Adu A.M. Wasike
Wandera Ogana
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.
author_facet Adu A.M. Wasike
Wandera Ogana
author_sort Adu A.M. Wasike
title 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_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_sort periodic solutions of a system of delay differential equations for a small delay
publisher Sultan Qaboos University
series Sultan Qaboos University Journal for Science
issn 1027-524X
2414-536X
publishDate 2002-06-01
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.
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
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