Hamiltonian control to desynchronize Kuramoto oscillators with higher-order interactions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908284650258432 |
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| author | Moriamé, Martin Lucas, Maxime Carletti, Timoteo |
| author_facet | Moriamé, Martin Lucas, Maxime Carletti, Timoteo |
| contents | Synchronization is a ubiquitous phenomenon in nature. Although it is necessary for the functioning of many systems, too much synchronization can also be detrimental, e.g., (partially) synchronized brain patterns support high-level cognitive processes and bodily control, but hypersynchronization can lead to epileptic seizures and tremors, as in neurodegenerative conditions such as Parkinson's disease.
Consequently, a critical research question is how to develop effective pinning control methods capable to reduce or modulate synchronization as needed.
Although such methods exist to control pairwise-coupled oscillators, there are none for higher-order interactions, despite the increasing evidence of their relevant role in brain dynamics.
In this work, we fill this gap by proposing a generalized control method designed to desynchronize Kuramoto oscillators connected through higher-order interactions. Our method embeds a higher-order Kuramoto model into a suitable Hamiltonian flow, and builds up on previous work in Hamiltonian control theory to analytically construct a feedback control mechanism.
We numerically show that the proposed method effectively prevents synchronization in synthetics and empirical higher-order networks. Although our findings indicate that pairwise contributions in the feedback loop are often sufficient, the higher-order generalization becomes crucial when pairwise coupling is weak. Finally, we explore the minimum number of controlled nodes required to fully desynchronize oscillators coupled via an all-to-all hypergraphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_13578 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hamiltonian control to desynchronize Kuramoto oscillators with higher-order interactions Moriamé, Martin Lucas, Maxime Carletti, Timoteo Dynamical Systems Optimization and Control Adaptation and Self-Organizing Systems Synchronization is a ubiquitous phenomenon in nature. Although it is necessary for the functioning of many systems, too much synchronization can also be detrimental, e.g., (partially) synchronized brain patterns support high-level cognitive processes and bodily control, but hypersynchronization can lead to epileptic seizures and tremors, as in neurodegenerative conditions such as Parkinson's disease. Consequently, a critical research question is how to develop effective pinning control methods capable to reduce or modulate synchronization as needed. Although such methods exist to control pairwise-coupled oscillators, there are none for higher-order interactions, despite the increasing evidence of their relevant role in brain dynamics. In this work, we fill this gap by proposing a generalized control method designed to desynchronize Kuramoto oscillators connected through higher-order interactions. Our method embeds a higher-order Kuramoto model into a suitable Hamiltonian flow, and builds up on previous work in Hamiltonian control theory to analytically construct a feedback control mechanism. We numerically show that the proposed method effectively prevents synchronization in synthetics and empirical higher-order networks. Although our findings indicate that pairwise contributions in the feedback loop are often sufficient, the higher-order generalization becomes crucial when pairwise coupling is weak. Finally, we explore the minimum number of controlled nodes required to fully desynchronize oscillators coupled via an all-to-all hypergraphs. |
| title | Hamiltonian control to desynchronize Kuramoto oscillators with higher-order interactions |
| topic | Dynamical Systems Optimization and Control Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2409.13578 |