Hybrid-type synchronization transitions: Where incipient oscillations, scale-free avalanches, and bistability live together

The human cortex is never at rest but in a state of sparse and noisy neural activity. It has been conjectured that such a state is best described as a critical dynamical process -- whose nature is still not fully understood -- where scale-free avalanches of activity emerge at the edge of a synchronization phase transition. Using a simple model of coupled excitable oscillators, we rule out standard phase transitions to explain the emergence of collective oscillations, as they do not suffice to explain current experimental evidence. Conversely, we uncover a novel hybrid-type of synchronization transition displaying a very-rich dynamical repertoire supporting all key empirical observations, including scale-free avalanches, marginal coherence, and bistability.