Interacting oscillators in complex networks: synchronization and the emergence of scale-free topologies

In natural systems, many processes can be represented as the result of the interaction of self-sustained oscillators on top of complex topological wirings of connections. We review some of the main results on the setting of collective (synchronized) behaviors in globally and locally identical coupled oscillators, and then discuss in more detail the main formalism that gives the necessary condition for the stability of a synchronous motion. Finally, we also briefly describe a case of a growing network of nonidentical oscillators, where the growth process is entirely guided by dynamical rules, and where the final synchronized state is accompanied with the emergence of a specific statistical feature (the scale-free property) in the network's degree distribution.