Plenary Talk

Collective states of networked phase oscillators: from explosive synchronization to Bellerophon states

November 23, 9:00-11:00 Am, Central Time 

Stefano Boccaletti

Senior research scientist,
CNR-Institute of Complex Systems,Florence, Italy;
Northwestern Polytechnical University, Xi'an, China

Abstract: The talk will describe spontaneous emergence of collective dynamics in networked phase oscillators. As a first step, I will discuss how synchronization may emerge in a graph. Synchronization is a process in which dynamical systems adjust some properties of their trajectories (due to their interactions, or to a driving force) so that they eventually operate in a macroscopically coherent way. A common result is that the vast majority of transitions to synchronization are of the second-order type, continuous and reversible. However, as soon as networked units with complex architectures of interaction are taken into consideration, abrupt and irreversible phenomena may take place, namely explosive synchronization,which rather remind first-order like transitions. In the second part of my talk, I will concentrate on a recently unveiled coherent state, the Bellerophon state, which is generically observed in the proximity of explosive synchronization at intermediate values of the coupling strength. Bellerophon states are multi-clustered states emerging in symmetric pairs. In these states, oscillators belonging to a given cluster are not locked in their instantaneous phases nor in their frequencies, rather they display the same long-time average frequency (a sort of effective global frequency). Moreover, Bellerophon states feature quantum traits, in that such average frequencies are all odd multiples of a fundamental rhythm.