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

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 sized 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.