Dynamic topology and percolation criticality in higher-order activity–vulnerability driven networks

The study of temporal higher-order networks is crucial for forecasting phenomena such as information spread and systemic resilience. However, previous dominant models like the higher-order activity-driven framework capture connection formation but overlook the crucial role of dissolution in network dynamics. This omission biases predictions of network evolution and stability. In this article, we introduce the higher-order activity-vulnerability driven (HOAVD) networks, a novel framework that simultaneously captures hyperedge formation and dissolution by activity and vulnerability of nodes. We show that the competition between these two attributes induces a gradual dynamic phase transition at a characteristic timescale, separating the dynamics into a short-timescale, activity-dominated regime and a long-timescale, balanced regime. Meanwhile, we obtain analytical expressions of topological property of HOAVD networks. Moreover, we derive an critical balance condition for system-wide percolation in the balanced regime. This condition reveals that the connectivity is sensitively constrained by the statistical interplay between the distributions of activity and vulnerability, a phenomenon representing a fundamental mechanism that was invisible to previous models. Our analytical results, which also provide insights into the time-dependent topology, are supported by numerical simulations of real data. Therefore, the HOAVD framework offers a more complete and physically grounded foundation for predicting and controlling dynamics in social, biological, and technological systems.