  An Ott-Antonsen reduced $M$-population of Kuramoto-Sakaguchi oscillators is
investigated, focusing on the influence of the phase-lag parameter $\alpha$ on
the collective dynamics. For oscillator populations coupled on a ring, we
obtained a wide variety of spatiotemporal patterns, including coherent states,
traveling waves, partially synchronized states, modulated states, and
incoherent states. Back-and-forth transitions between these states are found,
which suggest metastability. Linear stability analysis reveals the stable
regions of coherent states with different winding numbers $q$. Within certain
$\alpha$ ranges, the system settles into stable traveling wave solutions
despite the coherent states also being linearly stable. For around $\alpha
\approx 0.46\pi$, the system displays the most frequent metastable transitions
between coherent states and partially synchronized states, while for $\alpha$
closer to $\pi/2$, metastable transitions arise between partially synchronized
states and modulated states. This model captures metastable dynamics akin to
brain activity, offering insights into the synchronization of brain networks.
