  The spontaneous emergence of coherent behavior through synchronization plays
a key role in neural function, and its anomalies often lie at the basis of
pathologies. Here we employ a parsimonious (mesoscopic) approach to study
analytically and computationally the synchronization (Kuramoto) dynamics on the
actual human-brain connectome network. We elucidate the existence of a
so-far-uncovered intermediate phase, placed between the standard synchronous
and asynchronous phases, i.e. between order and disorder. This novel phase
stems from the hierarchical modular organization of the connectome. Where one
would expect a hierarchical synchronization process, we show that the interplay
between structural bottlenecks and quenched intrinsic frequency heterogeneities
at many different scales, gives rise to frustrated synchronization,
metastability, and chimera-like states, resulting in a very rich and complex
phenomenology. We uncover the origin of the dynamic freezing behind these
features by using spectral graph theory and discuss how the emerging complex
synchronization patterns relate to the need for the brain to access --in a
robust though flexible way-- a large variety of functional attractors and
dynamical repertoires without ad hoc fine-tuning to a critical point.
