  We show that excitability is generic in systems displaying dissipative
solitons when spatial inhomogeneities and drift are present. Thus, dissipative
solitons in systems which do not have oscillatory states, such as the
prototypical Swift-Hohenberg equation, display oscillations and Type I and II
excitability when adding inhomogeneities and drift to the system. This rich
dynamical behavior arises from the interplay between the pinning to the
inhomogeneity and the pulling of the drift. The scenario presented here
provides a general theoretical understanding of oscillatory regimes of
dissipative solitons reported in semiconductor microresonators. Our results
open also the possibility to observe this phenomenon in a wide variety of
physical systems.
