Abstract:
ABSTRACT: We prove the existence of an asymptotically stable periodic solution of a system of
delay differential equations with a small time delay τ > 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 τ = 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: Periodic Solutions, Delay Differential Equations, Schauder’s Fixed Point Theorem.
