标题： Dirac-Bianconi驱动振荡器的同步 显示英文标题

标题： Synchronization of Dirac-Bianconi driven oscillators

摘要： 在网络上的动力系统中，将动力学分配给节点，然后通过链接进行耦合。 这种方法不考虑群体相互作用以及链接和其他高维结构上的动力学。 高阶网络理论通过考虑定义在节点、链接、三角形和更高阶单形上的变量来解决这个问题，这些变量称为拓扑信号（或上链）。 此外，不同维度的拓扑信号可以通过狄拉克-比安科尼算子相互作用，该算子允许在例如节点和链接上定义的拓扑信号之间进行耦合。 这种相互作用可以引发各种动力学行为，例如周期性振荡。 振荡系统由在节点和链接上的拓扑信号组成，其动力学由狄拉克-比安科尼耦合驱动，因此我们称其为狄拉克-比安科尼驱动振荡器。 使用相位约简方法，我们得到了该系统的相位描述，并将其应用于研究两个此类振荡器之间的同步性。 这种方法提供了一种超越基于节点范式的高阶网络中振荡行为的分析方式，同时为节点和边信号提供了灵活的建模工具。 显示英文摘要

摘要： In dynamical systems on networks, one assigns the dynamics to nodes, which are then coupled via links. This approach does not account for group interactions and dynamics on links and other higher dimensional structures. Higher-order network theory addresses this by considering variables defined on nodes, links, triangles, and higher-order simplices, called topological signals (or cochains). Moreover, topological signals of different dimensions can interact through the Dirac-Bianconi operator, which allows coupling between topological signals defined, for example, on nodes and links. Such interactions can induce various dynamical behaviors, for example, periodic oscillations. The oscillating system consists of topological signals on nodes and links whose dynamics are driven by the Dirac-Bianconi coupling, hence, which we call it Dirac-Bianconi driven oscillator. Using the phase reduction method, we obtain a phase description of this system and apply it to the study of synchronization between two such oscillators. This approach offers a way to analyze oscillatory behaviors in higher-order networks beyond the node-based paradigm, while providing a ductile modeling tool for node- and edge-signals.