Periodic solutions for functional differential equations with periodic delay close to zero
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Date
2006-11-09
Authors
Hbid, My Lhassan
Qesmi, Redouane
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
This paper studies the existence of periodic solutions to the delay differential equation
ẋ(t) = ƒ(x(t - μτ(t)), ɛ).
The analysis is based on a perturbation method previously used for retarded differential equations with constant delay. By transforming the studied equation into a perturbed non-autonomous ordinary equation and using a bifurcation result and the Poincaré procedure for this last equation, we prove the existence of a branch of periodic solutions, for the periodic delay equation bifurcating from μ = 0.
Description
Keywords
Differential equation, Periodic delay, Bifurcation, h-asymptotic stability, Periodic solution
Citation
Hbid, M. L., & Qesmi, R. (2006). Periodic solutions for functional differential equations with periodic delay close to zero. <i>Electronic Journal of Differential Equations, 2006</i>(141), pp. 1-12.
Rights
Attribution 4.0 International