Neuhäuser Leonie, Mellor Andrew, Lambiotte Renaud
Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom and Hertie School, Berlin 10117, Germany.
Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom.
Phys Rev E. 2020 Mar;101(3-1):032310. doi: 10.1103/PhysRevE.101.032310.
Multibody interactions can reveal higher-order dynamical effects that are not captured by traditional two-body network models. In this work, we derive and analyze models for consensus dynamics on hypergraphs, where nodes interact in groups rather than in pairs. Our work reveals that multibody dynamical effects that go beyond rescaled pairwise interactions can appear only if the interaction function is nonlinear, regardless of the underlying multibody structure. As a practical application, we introduce a specific nonlinear function to model three-body consensus, which incorporates reinforcing group effects such as peer pressure. Unlike consensus processes on networks, we find that the resulting dynamics can cause shifts away from the average system state. The nature of these shifts depends on a complex interplay between the distribution of the initial states, the underlying structure, and the form of the interaction function. By considering modular hypergraphs, we discover state-dependent, asymmetric dynamics between polarized clusters where multibody interactions make one cluster dominate the other.
多体相互作用可以揭示传统两体网络模型无法捕捉到的高阶动力学效应。在这项工作中，我们推导并分析了超图上的一致性动力学模型，其中节点以组而非对的形式进行交互。我们的工作表明，只有当相互作用函数是非线性时，才会出现超越重新缩放的两体相互作用的多体动力学效应，而与潜在的多体结构无关。作为一个实际应用，我们引入了一个特定的非线性函数来对三体一致性进行建模，该函数纳入了诸如同伴压力等增强群体效应。与网络上的一致性过程不同，我们发现由此产生的动力学可以导致系统状态偏离平均状态。这些偏移的性质取决于初始状态的分布、潜在结构和相互作用函数的形式之间的复杂相互作用。通过考虑模块化超图，我们发现了极化簇之间依赖于状态的不对称动力学，其中多体相互作用使一个簇主导另一个簇。
