Spontanenous synchronization in complex networks

Spontaneous synchronization is the process through which a population of coupled oscillators reaches a state of global synchronization without a centralized driving mechanism. Examples include the synchronization of flashing fireflies and of cells in the heart and the brain.

The Kuramoto model consists of a population of oscillators whose phases are coupled to the each other along the edges of the complete graph and are subjected to noise. There exists an order parameter distinguishing a “desynchronized” phase, where each oscillator proceeds at its own natural frequency, from a “synchronized” phase, where a finite fraction of the oscillators becomes locked in phase. One goal of this project is to study

the situation in which the interactions among the oscillators are arranged along the edges of a general network. 

When the network has an intricate topology, the Kuramoto model (and its extensions) can lead to rich behavior that is not captured by the synchronized versus desynchronized dichotomy alone. In particular, if the network has a modular structure, in which different communities of nodes are more densely connected internally than with the rest of the network, then synchronization occurs over a hierarchy of different time scales. This means that first oscillators within each community synchronize, after that communities of communities synchronize, and so on.  Another  goal of the project is to analyse empirical network data and run simulations of the model on different structures. Thus, the project requires both analytical and computational work. 

Diego Garlaschelli,  Frank den Hollander, Joke Meijer

Janusz Meyhlan