Delay-periodic solutions and their stability using averaging in delay-differential equations, with applications

Authors

Thomas W. Carr, Southern Methodist UniversityFollow
Richard Haberman, Southern Methodist UniversityFollow
Thomas Erneux, Universite Libre de BruxellesFollow

Publication Date

2012

Abstract

Using the method of averaging we analyze periodic solutions to delay-differential equations, where the period is near to the value of the delay time (or a fraction thereof). The difference between the period and the delay time defines the small parameter used in the perturbation method. This allows us to consider problems with arbitrarily size delay times or of the delay term itself. We present a general theory and then apply the method to a specific model that has application in disease dynamics and lasers.

Document Type

Article

Keywords

differential equations, delay, averaging, periodic

Disciplines

Dynamic Systems | Non-linear Dynamics

Extent

14 pages

Format

.pdf

Language

English

Recommended Citation

Carr, Thomas W.; Haberman, Richard; and Erneux, Thomas, "Delay-periodic solutions and their stability using averaging in delay-differential equations, with applications" (2012). Mathematics Research. 1.
https://scholar.smu.edu/hum_sci_mathematics_research/1