Networked dynamic systems with higher-order interactions: stability versus complexity

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.