Metastability of multi-population Kuramoto-Sakaguchi oscillators

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 approximate to 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.