Proximity to Explosive Synchronization Determines Network Collapse and Recovery Trajectories in Neural and Economic...

When complex systems move away from criticality-a balance between order and chaos-they are no longer optimized. Furthermore, when criticality is lost too quickly, or recovery is delayed, system damage can result. However, the mechanism for these abnormally fast or slow critical transitions remains unknown. Here, we show that the proximity of a complex network to explosive synchronization (ES), a first-order phase transition, determines the trajectories of criticality loss and recovery after perturbations. Our computational models revealed characteristic dynamics based on network proximity to ES, enabling us to infer network phase transition types from empirical data and predict criticality transition patterns. We validated our predictions using empirical data from the human brain under anesthesia and the stock market during an economic crisis, demonstrating that early and prolonged recoveries can be systematically predicted. This study has implications for designing resilient networks that withstand perturbations and recover quickly.