Synchronization, diversity, and topology of networks of integrate and fireoscillators

We study synchronization dynamics of a population of pulse-coupled oscillat ors. In particular, we focus our attention on the interplay between topolog ical disorder and synchronization features of networks. First, we analyze s ynchronization time T in random networks, and find a scaling law which rela tes T to network; connectivity. Then, we compare synchronization time for s everal other topological configurations, characterized by a different degre e of randomness. The analysis shows that regular lattices perform better th an a disordered network. This fact can be understood by considering the var iability in the number of links between two adjacent neighbors. This phenom enon is equivalent to having a nonrandom topology with a distribution of in teractions and it can be removed by an adequate local normalization of the couplings.