Abstract
An Ott–Antonsen reduced M-population of Kuramoto–Sakaguchi oscillators is investigated, focusing on the influence of the phase-lag parameter α 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 α ranges, the system settles into stable traveling wave solutions despite the coherent states also being linearly stable. For around α≈0.46π, the system displays the most frequent metastable transitions between coherent states and partially synchronized states, while for α closer to π/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.
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