Bifurcations in the Kuramoto model with external forcing and higher-order interactions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909453078495232 |
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| author | Costa, Guilherme S. Novaes, Marcel de Aguiar, Marcus A. M. |
| author_facet | Costa, Guilherme S. Novaes, Marcel de Aguiar, Marcus A. M. |
| contents | Synchronization is an important phenomenon in a wide variety of systems comprising interacting oscillatory units, whether natural (like neurons, biochemical reactions, cardiac cells) or artificial (like metronomes, power grids, Josephson junctions). The Kuramoto model provides a simple description of these systems and has been useful in their mathematical exploration. Here we investigate this model combining two common features that have been observed in many systems: external periodic forcing and higher-order interactions among the elements. We show that the combination of these ingredients leads to a very rich bifurcation scenario that produces 11 different asymptotic states of the system, with competition between forced and spontaneous synchronization. We found, in particular, that saddle-node, Hopf and homoclinic manifolds are duplicated in regions of parameter space where the unforced system displays bi-stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08736 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bifurcations in the Kuramoto model with external forcing and higher-order interactions Costa, Guilherme S. Novaes, Marcel de Aguiar, Marcus A. M. Adaptation and Self-Organizing Systems Dynamical Systems Physics and Society Synchronization is an important phenomenon in a wide variety of systems comprising interacting oscillatory units, whether natural (like neurons, biochemical reactions, cardiac cells) or artificial (like metronomes, power grids, Josephson junctions). The Kuramoto model provides a simple description of these systems and has been useful in their mathematical exploration. Here we investigate this model combining two common features that have been observed in many systems: external periodic forcing and higher-order interactions among the elements. We show that the combination of these ingredients leads to a very rich bifurcation scenario that produces 11 different asymptotic states of the system, with competition between forced and spontaneous synchronization. We found, in particular, that saddle-node, Hopf and homoclinic manifolds are duplicated in regions of parameter space where the unforced system displays bi-stability. |
| title | Bifurcations in the Kuramoto model with external forcing and higher-order interactions |
| topic | Adaptation and Self-Organizing Systems Dynamical Systems Physics and Society |
| url | https://arxiv.org/abs/2409.08736 |