Rotating clusters in phase-lagged Kuramoto oscillators with higher-order interactions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866929230511603712 |
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| author | Moyal, Bhuwan Rajwani, Priyanka Dutta, Subhasanket Jalan, Sarika |
| author_facet | Moyal, Bhuwan Rajwani, Priyanka Dutta, Subhasanket Jalan, Sarika |
| contents | The effect of phase-lag parameter in pairwise interactions has been a topic of great interest for long. However, real-world systems often have interactions that are beyond pairwise and can be modeled using simplicial complexes. We investigate the effect of the inclusion of phase-lag in coupled Kuramoto oscillators with simplicial interactions and find that it shifts the critical points at which first-order transition from cluster synchronized state to incoherent state occurs. In the thermodynamic limit, using the Ott-Antonsen approach we derive a reduced equation for order parameter measuring cluster synchronization. Further, we progress through the self-consistency method to achieve a closed form of the order parameter measuring global synchronization which was lacking in Ott-Antonsen approach. Moreover, considering polar coordinates framework we obtain rotation frequency of the clusters which comes out to be a function of the phase-lag parameter further indicating that phase-lag can be used as a control parameter to achieve a desired cluster frequency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_14683 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rotating clusters in phase-lagged Kuramoto oscillators with higher-order interactions Moyal, Bhuwan Rajwani, Priyanka Dutta, Subhasanket Jalan, Sarika Adaptation and Self-Organizing Systems The effect of phase-lag parameter in pairwise interactions has been a topic of great interest for long. However, real-world systems often have interactions that are beyond pairwise and can be modeled using simplicial complexes. We investigate the effect of the inclusion of phase-lag in coupled Kuramoto oscillators with simplicial interactions and find that it shifts the critical points at which first-order transition from cluster synchronized state to incoherent state occurs. In the thermodynamic limit, using the Ott-Antonsen approach we derive a reduced equation for order parameter measuring cluster synchronization. Further, we progress through the self-consistency method to achieve a closed form of the order parameter measuring global synchronization which was lacking in Ott-Antonsen approach. Moreover, considering polar coordinates framework we obtain rotation frequency of the clusters which comes out to be a function of the phase-lag parameter further indicating that phase-lag can be used as a control parameter to achieve a desired cluster frequency. |
| title | Rotating clusters in phase-lagged Kuramoto oscillators with higher-order interactions |
| topic | Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2307.14683 |