Forced frequency locking for differential equations with distributional forcings

Abstract

This paper deals with forced frequency locking, i.e., the behavior of periodic solutions to autonomous differential equations under the influence of small periodic forcings. We show 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 happens as in the case of smooth forcings, and we derive formulas for the locking cones and for the asymptotic phases as in the case of smooth forcings.