Dynamic resilience in complex networks

Many real-world systems comprise fundamental elements that exhibit mutual exclusion and alternating activation. Here, we develop a framework for the evolution of network structures that captures the behaviors of such systems. We define the dynamic resilience of temporal networks using variational rates to measure how the evolutionary trajectories of network structures diverge under perturbations. We show that perturbations to specific edges and states of mutually exclusive elements can cause evolutionary trajectories of network structures to deviate significantly from the original path. Furthermore, we demonstrate that traditional resilience factors do not affect dynamic resilience, which is instead governed by mutual exclusion within our framework. Our results advance the study of network resilience, particularly for networks with evolving structures, offering a novel perspective for identifying crucial perturbations within the context of the states of mutually exclusive elements.