Extreme synchronization events in a Kuramoto model: The interplay between resource constraints and explosive transitions.

Many living and artificial systems possess structural and dynamical properties of complex networks. One of the most exciting living networked systems is the brain, in which synchronization is an essential mechanism of its normal functioning. On the other hand, excessive synchronization in neural networks reflects undesired pathological activity, including various forms of epilepsy. In this context, network-theoretical approach and dynamical modeling may uncover deep insight into the origins of synchronization-related brain disorders. However, many models do not account for the resource consumption needed for the neural networks to synchronize. To fill this gap, we introduce a phenomenological Kuramoto model evolving under the excitability resource constraints. We demonstrate that the interplay between increased excitability and explosive synchronization induced by the hierarchical organization of the network forces the system to generate short-living extreme synchronization events, which are well-known signs of epileptic brain activity. Finally, we establish that the network units occupying the medium levels of hierarchy most strongly contribute to the birth of extreme events emphasizing the focal nature of their origin.