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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.16715 |
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| _version_ | 1866913638570262528 |
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| author | Fariello, Ricardo de Aguiar, Marcus A. M. |
| author_facet | Fariello, Ricardo de Aguiar, Marcus A. M. |
| contents | The study of higher order interactions in the dynamics of Kuramoto oscillators has been a topic of intense recent research. Arguments based on dimensional reduction using the Ott-Antonsen ansatz show that such interactions usually facilitate synchronization, giving rise to bi-stability and hysteresis. Here we show that three body interactions shift the critical coupling for synchronization towards higher values in all dimensions, except $D=2$, where a cancellation occurs. After the transition, three and four body interactions combine to facilitate synchronization. Similar to the 2-dimensional case, bi-stability and hysteresis develop for large enough higher order interactions. We show simulations in $D=3$ and $4$ to illustrate the dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16715 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Third order interactions shift the critical coupling in multidimensional Kuramoto models Fariello, Ricardo de Aguiar, Marcus A. M. Pattern Formation and Solitons The study of higher order interactions in the dynamics of Kuramoto oscillators has been a topic of intense recent research. Arguments based on dimensional reduction using the Ott-Antonsen ansatz show that such interactions usually facilitate synchronization, giving rise to bi-stability and hysteresis. Here we show that three body interactions shift the critical coupling for synchronization towards higher values in all dimensions, except $D=2$, where a cancellation occurs. After the transition, three and four body interactions combine to facilitate synchronization. Similar to the 2-dimensional case, bi-stability and hysteresis develop for large enough higher order interactions. We show simulations in $D=3$ and $4$ to illustrate the dynamics. |
| title | Third order interactions shift the critical coupling in multidimensional Kuramoto models |
| topic | Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2404.16715 |