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 on 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.

中文翻译：

---

具有高阶相互作用的网络动态系统：稳定性与复杂性

复杂系统的稳定性深受底层结构的影响，底层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交互。然而，此类网络无法对具有两个以上节点之间的高阶交互的网络系统的整体复杂性进行编码。集合结构提供了对成对和高阶交互的自然描述，其中节点根据其共享特征分为多个集合。在这里，我们通过采用集合结构推导出具有高阶交互的网络系统的稳定性标准。特别是，我们提供了一个简单的规则，表明高阶交互对社区稳定性具有双面作用——如果任何两个节点的公共集的预期数量小于 1，则具有集合结构的网络系统会稳定。此外，尽管先前的知识表明更多的交互（即复杂性）会破坏网络系统的稳定性，但我们报告说，通过高阶交互，网络系统可以通过形成更多的局部集来稳定。我们的研究结果在程度异质结构、不同的平衡状态和相互作用类型方面是稳健的。