Controllability Robustness of Simplicial Complexes

This article explores the controllability robustness of simplicial complexes under both node-based and edge-based attacks. By considering network topology, dynamical properties, and higher order interactions, we propose a universal nodal dynamical model applicable to simplicial complexes of arbitrary dimensions. Quantitative analysis reveals that both the quantity and spatial distribution of 2-simplices play a pivotal role in regulating the robustness of network controllability. These results highlight the critical impact of second-order interaction structures on network robustness and suggest that the underlying mechanisms, such as higher order topological connectivity and dynamical synergy, can be extended to elucidate how higher dimensional $q$ -simplices ( $q\gt 2$ ) influence controllability robustness.