Wang Ye, Li Aming, Wang Long
Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, China.
Center for Multi-Agent Research, Institute for Artificial Intelligence, Peking University, Beijing 100871, China.
Natl Sci Rev. 2024 Mar 18;11(9):nwae103. doi: 10.1093/nsr/nwae103. eCollection 2024 Sep.
The stability of complex systems is profoundly affected by underlying structures, which are often modeled as networks where nodes indicate system components and edges indicate pairwise interactions between nodes. However, such networks cannot encode the overall complexity of networked systems with higher-order interactions among more than two nodes. Set structures provide a natural description of pairwise and higher-order interactions where nodes are grouped into multiple sets based on their shared traits. Here we derive the stability criteria for networked systems with higher-order interactions by employing set structures. In particular, we provide a simple rule showing that the higher-order interactions play a double-sided role in community stability-networked systems with set structures are stabilized if the expected number of common sets for any two nodes is less than one. Moreover, although previous knowledge suggests that more interactions (i.e. complexity) destabilize networked systems, we report that, with higher-order interactions, networked systems can be stabilized by forming more local sets. Our findings are robust with respect to degree heterogeneous structures, diverse equilibrium states and interaction types.
复杂系统的稳定性深受潜在结构的影响，这些潜在结构通常被建模为网络，其中节点表示系统组件，边表示节点之间的成对相互作用。然而，这样的网络无法编码具有两个以上节点之间高阶相互作用的网络系统的整体复杂性。集合结构提供了一种对成对和高阶相互作用的自然描述，其中节点基于它们的共享特征被分组到多个集合中。在这里，我们通过采用集合结构推导了具有高阶相互作用的网络系统的稳定性标准。特别地，我们提供了一个简单规则，表明高阶相互作用在群落稳定性中起着双面作用——如果任意两个节点的公共集合的预期数量小于1，则具有集合结构的网络系统是稳定的。此外，尽管先前的知识表明更多的相互作用（即复杂性）会使网络系统不稳定，但我们报告称，在存在高阶相互作用的情况下，网络系统可以通过形成更多的局部集合来实现稳定。我们的发现对于度异质结构、多样的平衡态和相互作用类型具有鲁棒性。
