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 nonlinearities 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.

许多动力学系统的基本交互单元涉及两个以上的节点。在这样的情况下，网络不是合适的建模框架，最近转向包括超图在内的高阶模型变得越来越流行。在本文中，我们探索了关于超图的共识的非线性动力学，从而允许在任何基数的超边缘内进行交互。在讨论了将非线性纳入动态模型的不同方法之后，我们基于不同的社会学理论，探索了其数学特性，并进行了仿真研究以进行数值研究。在关注合成超图（即块超图）之后，我们研究了真实结构的动力学，并详细探讨了参与和固执对极化的作用。