Optimal interaction functions realizing higher-order Kuramoto dynamics with arbitrary limit-cycle oscillators
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910024266153984 |
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| author | Namura, Norihisa Muolo, Riccardo Nakao, Hiroya |
| author_facet | Namura, Norihisa Muolo, Riccardo Nakao, Hiroya |
| contents | The Kuramoto model is the simplest case of globally coupled phase oscillators with a purely sinusoidal fundamental-harmonic phase coupling function, whose dynamical properties have been extensively studied. While coupled phase oscillators are derived from weakly interacting limit-cycle oscillators via phase reduction, this procedure does not necessarily yield the Kuramoto model or its higher-order extensions exactly for general limit-cycle oscillators and interaction functions, except in the special case of interacting Stuart-Landau oscillators. In this study, we artificially design optimal pairwise and higher-order interaction functions between limit-cycle oscillators, from which higher-order Kuramoto models can be exactly derived via phase reduction for arbitrary smooth limit-cycle oscillators. We validate the results through numerical simulations of FitzHugh-Nagumo oscillators, demonstrating that the collective synchronization dynamics predicted by the reduced higher-order Kuramoto models are realized. Control of the collective phase of the FitzHugh-Nagumo oscillators based on Ott-Antonsen reduction of the higher-order Kuramoto model is also demonstrated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14501 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal interaction functions realizing higher-order Kuramoto dynamics with arbitrary limit-cycle oscillators Namura, Norihisa Muolo, Riccardo Nakao, Hiroya Adaptation and Self-Organizing Systems The Kuramoto model is the simplest case of globally coupled phase oscillators with a purely sinusoidal fundamental-harmonic phase coupling function, whose dynamical properties have been extensively studied. While coupled phase oscillators are derived from weakly interacting limit-cycle oscillators via phase reduction, this procedure does not necessarily yield the Kuramoto model or its higher-order extensions exactly for general limit-cycle oscillators and interaction functions, except in the special case of interacting Stuart-Landau oscillators. In this study, we artificially design optimal pairwise and higher-order interaction functions between limit-cycle oscillators, from which higher-order Kuramoto models can be exactly derived via phase reduction for arbitrary smooth limit-cycle oscillators. We validate the results through numerical simulations of FitzHugh-Nagumo oscillators, demonstrating that the collective synchronization dynamics predicted by the reduced higher-order Kuramoto models are realized. Control of the collective phase of the FitzHugh-Nagumo oscillators based on Ott-Antonsen reduction of the higher-order Kuramoto model is also demonstrated. |
| title | Optimal interaction functions realizing higher-order Kuramoto dynamics with arbitrary limit-cycle oscillators |
| topic | Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2510.14501 |