Complex self-sustained oscillation patterns in modular excitable networks

Abstract

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.