Many systems in Nature, like neurons and heart cells, exhibit a behavior known as excitability, that is characterized by an all-or-none response to external stimuli with respect to a threshold. This property confers neurons with certain computational capabilities. From the viewpoint of dynamical systems theory the simplest scenario consists of a fixed point close to certain oscillatory instabilities. One observes two different manifestations of excitability depending on the oscillatory bifurcation involved: Types I and II depending on whether zero frequency responses are possible or not, respectively. In recent studies we have characterized the excitable behavior of Localized Structures (LSs) in dissipative nonlinear media. Interestingly, one is able to perform universal computations with excitable LSs. Having in mind the applicability of excitable LSs, a drawback is that generically LSs do not exhibit oscillatory instabilities.
In the present work we present a scenario in which the presence of spatial inhomogeneities and drift makes LSs excitable. Thus, systems which do not exhibit oscillatory LSs, including gradient systems 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 LSs reported in semiconductor microresonators. Our results open also the possibility to observe this phenomenon in a wide variety of physical systems.