Metastability of multi-population Kuramoto-Sakaguchi oscillators
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| Format: | Preprint |
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2024
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| _version_ | 1866929657873432576 |
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| author | Li, Bojun Uchida, Nariya |
| author_facet | Li, Bojun Uchida, Nariya |
| contents | 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 $α\approx 0.46π$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_15396 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Metastability of multi-population Kuramoto-Sakaguchi oscillators Li, Bojun Uchida, Nariya Adaptation and Self-Organizing Systems 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 $α\approx 0.46π$, 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. |
| title | Metastability of multi-population Kuramoto-Sakaguchi oscillators |
| topic | Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2405.15396 |