Synchronization of phase oscillators on complex hypergraphs
Synchronization of phase oscillators on complex hypergraphs
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DOI：
10.1063/5.0116747
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发表时间：
2023-03-01
期刊：
影响因子：
2.9
通讯作者：
Skardal, Per Sebastian
中科院分区：
文献类型：
--
作者：
Adhikari, Sabina;Restrepo, Juan G. G.;Skardal, Per Sebastian
我们研究结构化高阶相互作用对耦合相位振荡器集体行为的影响。通过将超图生成模型与降维技术相结合，我们获得了系统阶参数的简化微分方程组。我们以超边尺寸为 2（链接）和 3（三角形）的超图为例来说明我们的框架。对于这种情况，我们获得了一组阶次参数的两个耦合非线性代数方程。对于通过三角形耦合的强值，系统表现出双稳态和爆炸性同步转换。我们找到了导致超图性质双稳态的条件，并通过数值模拟验证了我们的预测。我们的结果提供了一个研究超图中相位振荡器同步的通用框架，并且它们可以扩展到具有任意大小的超边、动态结构相关性和其他特征的超图。
We study the effect of structured higher-order interactions on the collective behavior of coupled phase oscillators. By combining a hypergraph generative model with dimensionality reduction techniques, we obtain a reduced system of differential equations for the system's order parameters. We illustrate our framework with the example of a hypergraph with hyperedges of sizes 2 (links) and 3 (triangles). For this case, we obtain a set of two coupled nonlinear algebraic equations for the order parameters. For strong values of coupling via triangles, the system exhibits bistability and explosive synchronization transitions. We find conditions that lead to bistability in terms of hypergraph properties and validate our predictions with numerical simulations. Our results provide a general framework to study the synchronization of phase oscillators in hypergraphs, and they can be extended to hypergraphs with hyperedges of arbitrary sizes, dynamic-structural correlations, and other features.