Prolonged hysteresis in the Kuramoto model with inertia and higher-order interactions
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866917583626698752 |
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| author | Sabhahit, Narayan G. Khurd, Akanksha S. Jalan, Sarika |
| author_facet | Sabhahit, Narayan G. Khurd, Akanksha S. Jalan, Sarika |
| contents | The inclusion of inertia in the Kuramoto model has been long reported to change the nature of phase transition, providing a fertile ground to model the dynamical behaviors of interacting units. More recently, higher-order interactions have been realized as essential for the functioning of real-world complex systems ranging from the brain to disease spreading. Yet, analytical insights to decipher the role of inertia with higher-order interactions remain challenging. Here, we study the Kuramoto model with inertia on simplicial complexes, merging two research domains. We develop an analytical framework in a mean-field setting using self-consistent equations to describe the steady-state behavior, which reveals a prolonged hysteresis in the synchronization profile. Inertia and triadic interaction strength exhibit isolated influence on system dynamics by predominantly governing, respectively, the forward and backward transition points. This work sets a paradigm to deepen our understanding of real-world complex systems such as power grids modeled as the Kuramoto model with inertia. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_08363 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Prolonged hysteresis in the Kuramoto model with inertia and higher-order interactions Sabhahit, Narayan G. Khurd, Akanksha S. Jalan, Sarika Adaptation and Self-Organizing Systems The inclusion of inertia in the Kuramoto model has been long reported to change the nature of phase transition, providing a fertile ground to model the dynamical behaviors of interacting units. More recently, higher-order interactions have been realized as essential for the functioning of real-world complex systems ranging from the brain to disease spreading. Yet, analytical insights to decipher the role of inertia with higher-order interactions remain challenging. Here, we study the Kuramoto model with inertia on simplicial complexes, merging two research domains. We develop an analytical framework in a mean-field setting using self-consistent equations to describe the steady-state behavior, which reveals a prolonged hysteresis in the synchronization profile. Inertia and triadic interaction strength exhibit isolated influence on system dynamics by predominantly governing, respectively, the forward and backward transition points. This work sets a paradigm to deepen our understanding of real-world complex systems such as power grids modeled as the Kuramoto model with inertia. |
| title | Prolonged hysteresis in the Kuramoto model with inertia and higher-order interactions |
| topic | Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2303.08363 |