Coupled Networks, Patterns and Complexity - Abstract
Restrepo, Juan G.
In this talk I will describe synchronization in hierarchical networks of Kuramoto oscillators with M communities, in which oscillators in the same community are more strongly coupled than oscillators in different communities. By using the Ott-Antonsen Ansatz, the dynamics of the full system is reduced to that of M coupled planar oscillators, from which the degree of local synchrony in each community can be analyzed. In the limit when the number of communities M is large, a second dimensionality reduction is used to study the degree of synchrony between the different communities. Bifurcations between incoherence, local synchrony, and global synchrony are characterized using these lower dimensional systems. Depending on the relative strength of global and local coupling, the transition to synchrony can be mediated by local or global effects. The predictions of this theory, which assumes all-to-all connectivity within each community, describe quantitatively the transition to synchrony in modular Erdös-Rényi networks. Multiple hierarchical levels can be analyzed using the same method.