论文标题
使用超图的多体相互作用的网络扩散研究
A study of diffusion in network with multi-body interactions using Hypergraphs
论文作者
论文摘要
认识到各种复杂系统中多体相互作用的丰度，我们在这里研究了一种将多体相互作用纳入动态网络中的可能方法。采用超图作为基础体系结构有助于我们提出的动态网络模型，超越了仅成对相互作用的传统原型。我们介绍了一些与超图相关的矩阵，以将多体框架合并到动态网络中。我们说明了一个事实，即通过成对二进制相互作用对多体相互作用的近似，即将图视为相应的动态网络的基础结构可能会导致研究的错误结论。在这里，我们使用加权超图来处理可变权重的多体相互作用。我们研究离散和连续时间动力网络中全球和局部同步的可能性。结尾包括一些现实世界的数值插图，以增强我们的理论结果。
Being cognizant of the abundance of multi-body interactions in various complex systems, here we investigate a possible way to incorporate multi-body interactions in dynamical networks. Adopting hypergraph as the underlying architecture aids our proposed dynamical network models to go beyond the traditional archetype of only pairwise interactions. We introduce some matrices associated with hypergraphs to incorporate multi-body frameworks in dynamic networks. We illustrate the fact that the approximation of multi-body interactions by pairwise binary interactions, i.e. considering graph as the underlying architecture of the corresponding dynamical network may lead to a wrong conclusion to the study. Here we use weighted hypergraphs to deal with the multi-body interactions of variable weights. We study the possibility of global and local synchronization in discrete and continuous-time dynamical networks. Some real-world numerical illustrations are included at the end to reinforce our theoretical results.
