Forced Frequency Locking for Differential Equations with Distributional Forcings

We study the problem of forced frequency locking, i.e., the behavior of periodic solutions to autonomous differential equations under the influence of small periodic forcings. It is shown that, although the forcings are allowed to be discontinuous (e.g., step-function-like) or even distributional (e.g., Dirac-function-like), the forced frequency locking occurs as in the case of smooth forcings. Thus, the formulas for the locking cones and for the asymptotic phases are derived as in the case of smooth forcings.