  Networks of coupled oscillators can exhibit a wide range of complex dynamical
behavior, from complete synchronization to chimera and chaotic states. Here we
analyze the dynamics of networks of populations of heterogeneous mean-field
coupled Kuramoto-Sakaguchi oscillators and show that the instability that leads
to chimera states in a simple two-population model also leads to extensive
chaos in large networks of coupled populations. Formally, the system consists
of a complex network of interacting oscillator populations whose mesoscopic
behavior evolves according to the Ott-Antonsen equations. By considering
identical parameters across populations, the system contains a manifold of
homogeneous solutions where all populations behave identically. Stability
analysis of these homogeneous states provided by the Master Stability Function
shows that non-trivial dynamics might emerge on a wide region of the parameter
space for arbitrary network topologies. As examples, we first revisit the
two-population case, and provide a complete bifurcation diagram. Then, we
investigate the emergent dynamics in large ring and Erd\"os-R\'enyi networks.
In both cases, transverse instabilities lead to extensive space-time chaos,
i.e., irregular regimes whose complexity scales linearly with the system size.
In summary, our work provides a unified analytical framework to understand the
emergent dynamics of networks of Kuramoto populations, from chimera states to
robust high-dimensional chaos.
