论文标题
建模超图上的非线性共识动力学
Modelling Non-Linear Consensus Dynamics on Hypergraphs
论文作者
论文摘要
许多动态系统的基本相互作用单元涉及两个以上的节点。在网络不是合适的建模框架的情况下，它最近越来越流行地转向包括HyperGraphs的高阶模型。在本文中，我们探讨了在超图上共识的非线性动力学，从而使任何基数的高音中的相互作用都可以进行。在讨论了以不同社会学理论为基础的动态模型中，可以将非线性纳入非线性的不同方式之后，我们探索了其数学属性并执行模拟以数值研究。在重点关注合成超图（即块超图上）之后，我们研究了现实世界结构的动力学，并详细探讨了参与和固执在极化中的作用。
The basic interaction unit of many dynamical systems involves more than two nodes. In such situations where networks are not an appropriate modelling framework, it has recently become increasingly popular to turn to higher-order models, including hypergraphs. In this paper, we explore the non-linear dynamics of consensus on hypergraphs, allowing for interactions within hyperedges of any cardinality. After discussing the different ways in which non-linearities can be incorporated in the dynamical model, building on different sociological theories, we explore its mathematical properties and perform simulations to investigate them numerically. After focussing on synthetic hypergraphs, namely on block hypergraphs, we investigate the dynamics on real-world structures, and explore in detail the role of involvement and stubbornness on polarisation.
