Synchronization of identical oscillators on a sphere: exact results with external forces and higher-order interactions
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912389390139392 |
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| author | Costa, Guilherme S. Novaes, Marcel Fariello, Ricardo de Aguiar, Marcus A. M. |
| author_facet | Costa, Guilherme S. Novaes, Marcel Fariello, Ricardo de Aguiar, Marcus A. M. |
| contents | We study the dynamics of the Kuramoto model on the sphere under higher-order interactions and an external periodic force. For identical oscillators, we introduce a novel way to incorporate three- and four-body interactions into the dynamics of the order parameter, allowing for a full dimensional reduction of this system. We discuss how such reduction can be implemented in two different ways and how they are related. When restricted to the equator, the dynamics is similar to that of the usual Kuramoto model, up to an interesting renormalization of the coupling constants. Outside this plane, the motion reduces to a two-parameter set of periodic orbits. We also locate the bifurcation curves of the system as functions of different parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17255 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Synchronization of identical oscillators on a sphere: exact results with external forces and higher-order interactions Costa, Guilherme S. Novaes, Marcel Fariello, Ricardo de Aguiar, Marcus A. M. Adaptation and Self-Organizing Systems Physics and Society We study the dynamics of the Kuramoto model on the sphere under higher-order interactions and an external periodic force. For identical oscillators, we introduce a novel way to incorporate three- and four-body interactions into the dynamics of the order parameter, allowing for a full dimensional reduction of this system. We discuss how such reduction can be implemented in two different ways and how they are related. When restricted to the equator, the dynamics is similar to that of the usual Kuramoto model, up to an interesting renormalization of the coupling constants. Outside this plane, the motion reduces to a two-parameter set of periodic orbits. We also locate the bifurcation curves of the system as functions of different parameters. |
| title | Synchronization of identical oscillators on a sphere: exact results with external forces and higher-order interactions |
| topic | Adaptation and Self-Organizing Systems Physics and Society |
| url | https://arxiv.org/abs/2505.17255 |