论文标题
超图上的动力系统
Dynamical systems on Hypergraphs
论文作者
论文摘要
网络是一种广泛使用且有效的范式，用于建模基本单元成对相互作用的现实世界系统。许多身体互动通常都在发挥作用，不能通过诉诸二进制交换来建立模型。在这项工作中，我们考虑了锚定在HyperGraphs上的一般动态系统。任意尺寸的超核心理想地包围了单个单元，以便考虑多个同时的相互作用。后者是由在此引入和表征的组合拉普拉斯式介导的。主稳定函数的形式主义适合当前设置。研究图纹模式和非线性（常规和混乱）振荡器的同步，用于在超图上演变的一般系统。对外部施加的扰动的反应具有相互作用的高阶性质的烙印。
Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider a general class of dynamical systems anchored on hypergraphs. Hyperedges of arbitrary size ideally encircle individual units so as to account for multiple, simultaneous interactions. These latter are mediated by a combinatorial Laplacian, that is here introduced and characterised. The formalism of the Master Stability Function is adapted to the present setting. Turing patterns and the synchronisation of non linear (regular and chaotic) oscillators are studied, for a general class of systems evolving on hypergraphs. The response to externally imposed perturbations bears the imprint of the higher order nature of the interactions.
