  We study the relationship between the modularity of scale-free excitable
networks and their ability to support self-sustained oscillation patterns. We
find that the probability for a network of given degree-distribution exponent
to be able to support self-sustained oscillations is strongly affected by its
modularity. In addition, both high- and low-modularity networks are more likely
to exhibit long-period oscillation patterns than those with intermediate
modularity, but the degrees of complexity and correlation in these two cases
are different. The long-period oscillations cannot be explained by a
minimum-length Winfree loop, but instead arise from the interplay between two
or more propagating waves. Finally, we introduce a new method that can be used
to analyze the structure of the self-sustained oscillation sources at different
levels of detail and show that the period of the oscillation pattern is
statistically correlated with the fraction of modules that are part of the
oscillation source.
