Third order interactions shift the critical coupling in multidimensional Kuramoto models (2404.16715v2)
Abstract: The study of higher order interactions in the dynamics of Kuramoto oscillators has been a topic of intense recent research. Arguments based on dimensional reduction using the Ott-Antonsen ansatz show that such interactions usually facilitate synchronization, giving rise to bi-stability and hysteresis. Here we show that three body interactions shift the critical coupling for synchronization towards higher values in all dimensions, except $D=2$, where a cancellation occurs. After the transition, three and four body interactions combine to facilitate synchronization. Similar to the 2-dimensional case, bi-stability and hysteresis develop for large enough higher order interactions. We show simulations in $D=3$ and $4$ to illustrate the dynamics.
- Networks beyond pairwise interactions: Structure and dynamics. Physics Reports, 874:1–92, 2020.
- Homological scaffolds of brain functional networks. Journal of The Royal Society Interface, 11(101):20140873, 2014.
- Cliques and cavities in the human connectome. Journal of computational neuroscience, 44:115–145, 2018.
- Sparse low-order interaction network underlies a highly correlated and learnable neural population code. Proceedings of the National Academy of sciences, 108(23):9679–9684, 2011.
- Higher-order interactions stabilize dynamics in competitive network models. Nature, 548(7666):210–213, 2017.
- High-order interactions distort the functional landscape of microbial consortia. PLoS Biology, 17(12):e3000550, 2019.
- Higher-order organization of complex networks. Science, 353(6295):163–166, 2016.
- Social contagion models on hypergraphs. Physical Review Research, 2(2):023032, 2020.
- Simplicial models of social contagion. Nature communications, 10(1):2485, 2019.
- Simplicial sis model in scale-free uniform hypergraph. Journal of Statistical Mechanics: Theory and Experiment, 2019(12):123207, 2019.
- Fitness for synchronization of network motifs. Physica A: Statistical Mechanics and its Applications, 343:279–287, 2004.
- Vesna Berec. Chimera state and route to explosive synchronization. Chaos, Solitons & Fractals, 86:75–81, 2016.
- Abrupt desynchronization and extensive multistability in globally coupled oscillator simplexes. Physical review letters, 122(24):248301, 2019.
- Higher order interactions in complex networks of phase oscillators promote abrupt synchronization switching. Communications Physics, 3(1):218, 2020.
- Rotating clusters in phase-lagged kuramoto oscillators with higher-order interactions. Phys. Rev. E, 109:034211, Mar 2024. doi: 10.1103/PhysRevE.109.034211. URL https://link.aps.org/doi/10.1103/PhysRevE.109.034211.
- Symmetry-breaking higher-order interactions in coupled phase oscillators. Chaos, Solitons & Fractals, 181:114721, 2024.
- Low dimensional behavior of large systems of globally coupled oscillators. Chaos, 18(3):1–6, 2008. ISSN 10541500. doi: 10.1063/1.2930766.
- Continuous versus discontinuous transitions in the d-dimensional generalized kuramoto model: Odd d is different. Physical Review X, 9(1):011002, 2019.
- The kuramoto model on a sphere: Explaining its low-dimensional dynamics with group theory and hyperbolic geometry. Chaos: An Interdisciplinary Journal of Nonlinear Science, 31(9):093113, 2021.
- Hopf normal form with sn symmetry and reduction to systems of nonlinearly coupled phase oscillators. Physica D: Nonlinear Phenomena, 325:14–24, 2016.
- Ana Elisa D Barioni and Marcus AM de Aguiar. Complexity reduction in the 3d kuramoto model. Chaos, Solitons & Fractals, 149:111090, 2021.
- Exploring the phase diagrams of multidimensional kuramoto models. Chaos, Solitons & Fractals, 179:114431, 2024.
Sponsor
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.