Excitability of localized structures induced by spatial inhomogeneities and drift

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.