  Oscillatory complex networks in the metastable regime have been used to study
the emergence of integrated and segregated activity in the brain, which are
hypothesised to be fundamental for cognition. Yet, the parameters and the
underlying mechanisms necessary to achieve the metastable regime are hard to
identify, often relying on maximising the correlation with empirical functional
connectivity dynamics. Here, we propose and show that the brain's
hierarchically modular mesoscale structure alone can give rise to robust
metastable dynamics and (metastable) chimera states in the presence of phase
frustration. We construct unweighted $3$-layer hierarchical networks of
identical Kuramoto-Sakaguchi oscillators, parameterized by the average degree
of the network and a structural parameter determining the ratio of connections
between and within blocks in the upper two layers. Together, these parameters
affect the characteristic timescales of the system. Away from the critical
synchronization point, we detect the emergence of metastable states in the
lowest hierarchical layer coexisting with chimera and metastable states in the
upper layers. Using the Laplacian renormalization group flow approach, we
uncover two distinct pathways towards achieving the metastable regimes detected
in these distinct layers. In the upper layers, we show how the
symmetry-breaking states depend on the slow eigenmodes of the system. In the
lowest layer instead, metastable dynamics can be achieved as the separation of
timescales between layers reaches a critical threshold. Our results show an
explicit relationship between metastability, chimera states, and the eigenmodes
of the system, bridging the gap between harmonic based studies of empirical
data and oscillatory models.
