Multibody interactions and nonlinear consensus dynamics on networked systems.
Multibody interactions and nonlinear consensus dynamics on networked systems.
复制标题
网络系统上的多体相互作用和非线性一致性动力学。
DOI：
10.1103/physreve.101.032310
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
R. Lambiotte
中科院分区：
文献类型：
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作者：
Leonie Neuhäuser;A. Mellor;R. Lambiotte
多体相互作用可以揭示传统两体网络模型无法捕捉的高阶动力学效应。在这项工作中，我们推导和分析模型的共识动力学超图，其中节点相互作用的群体，而不是成对的。我们的工作表明，多体动力学效应，超越重新标度的成对相互作用可以出现，只有当相互作用函数是非线性的，无论潜在的多体结构。作为一个实际应用，我们引入了一个特定的非线性函数来模拟三体共识，其中包括增强群体效应，如同伴压力。与网络上的共识过程不同，我们发现由此产生的动态可能会导致偏离平均系统状态。这些变化的性质取决于初始状态的分布、底层结构和相互作用函数的形式之间的复杂相互作用。通过考虑模块超图，我们发现状态依赖，极化集群之间的非对称动力学多体相互作用，使一个集群占主导地位。
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.