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arXiv · 2405.15396

Metastability of multi-population Kuramoto-Sakaguchi oscillators

Bojun Li·Nariya Uchida
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Abstract

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.

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Bojun Li, Nariya Uchida. 2024-05-24. Metastability of multi-population Kuramoto-Sakaguchi oscillators. https://doi.org/10.1063/5.0220321

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