  Power-law-shaped avalanche-size distributions are widely used to probe for
critical behavior in many different systems, particularly in neural networks.
The definition of avalanche is ambiguous. Usually, theoretical avalanches are
defined as the activity between a stimulus and the relaxation to an inactive
absorbing state. On the other hand, experimental neuronal avalanches are
defined by the activity between consecutive silent states. We claim that the
latter definition may be extended to some theoretical models to characterize
their power-law avalanches and critical behavior. We study a system in which
the separation of driving and relaxation time scales emerges from its
structure. We apply both definitions of avalanche to our model. Both yield
power-law-distributed avalanches that scale with system size in the critical
point as expected. Nevertheless, we find restricted power-law-distributed
avalanches outside of the critical region within the experimental procedure,
which is not expected by the standard theoretical definition. We remark that
these results are dependent on the model details.
