All beauty, richness and harmony in the emergent dynamics of a complex system largely
depend on the specific way in which its elementary components interact. The last twenty-five …

Over the past two decades, complex network theory provided the ideal framework for
investigating the intimate relationships between the topological properties characterizing the …

Various systems in physics, biology, social sciences and engineering have been
successfully modeled as networks of coupled dynamical systems, where the links describe …

The emergence of synchronization in a network of coupled oscillators is a fascinating
subject of multidisciplinary research. This survey reviews the vast literature on the theory …

An imperative condition for the functioning of a power-grid network is that its power
generators remain synchronized. Disturbances can prompt desynchronization, which is a …

Traditionally, much of the study of networks has focused on structural features. Indeed,
mathematical subjects such as graph theory have a rich history of investigating network …

Investigating the dynamics of a network of oscillatory systems is a timely and urgent topic.
Phase synchronization has proven paradigmatic to study emergent collective behavior …

The dynamical systems found in nature are rarely isolated. Instead they interact and
influence each other. The coupling functions that connect them contain detailed information …

Inference of causality is central in nonlinear time series analysis and science in general. A
popular approach to infer causality between two processes is to measure the information …

We study optimal synchronization in networks of heterogeneous phase oscillators. Our main
result is the derivation of a synchrony alignment function that encodes the interplay between …