Abstract
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.
Keywords
Publication details
- DOI
- 10.24200/squjs.vol7iss2pp295-302
- Journal
- Sultan Qaboos University Journal for Science, 7(2), 295
- Publisher
- Sultan Qaboos University
- Open access
- Gold open access
- License
- CC BY 4.0
Cite this article
APA 7
Wasike, A. A., & Ogana, W. (2002). Periodic Solutions of a System of Delay Differential Equations for a Small Delay. Sultan Qaboos University Journal for Science, 7(2), 295. https://doi.org/10.24200/squjs.vol7iss2pp295-302
MLA 9
Wasike, Adu A.M., and Wandera Ogana. "Periodic Solutions of a System of Delay Differential Equations for a Small Delay." Sultan Qaboos University Journal for Science, vol. 7, no. 2, 2002, pp. 295. https://doi.org/10.24200/squjs.vol7iss2pp295-302.
Chicago (author–date)
Wasike, Adu A.M., and Wandera Ogana. 2002. "Periodic Solutions of a System of Delay Differential Equations for a Small Delay." Sultan Qaboos University Journal for Science 7 (2): 295. https://doi.org/10.24200/squjs.vol7iss2pp295-302.
Harvard
Wasike, A. A. and Ogana, W. (2002) 'Periodic Solutions of a System of Delay Differential Equations for a Small Delay', Sultan Qaboos University Journal for Science, 7(2), pp. 295. doi:10.24200/squjs.vol7iss2pp295-302.
Vancouver
Wasike AA, Ogana W. Periodic Solutions of a System of Delay Differential Equations for a Small Delay. Sultan Qaboos University Journal for Science. 2002;7(2):295. doi:10.24200/squjs.vol7iss2pp295-302
IEEE
A. A. Wasike, and W. Ogana, "Periodic Solutions of a System of Delay Differential Equations for a Small Delay," Sultan Qaboos University Journal for Science, vol. 7, no. 2, pp. 295, 2002, doi: 10.24200/squjs.vol7iss2pp295-302.