Dynamic Survivability Centrality in Nonlinear Oscillator Systems

In light of the fact that existing centrality indexes disregard the influence of dynamic characteristics and lack generalizability due to standard diversification, this study investigates dynamic survivability centrality, which enables quantification of oscillators’ capacity to impact the dynamic survivability of nonlinear oscillator systems. Taking an Erdős–Rényi random graph system consisting of Stuart–Landau oscillators as an illustrative example, the typical symmetry synchronization is considered as the key mission to be accomplished in light of the study and the dynamic survivability centrality value is found to be dependent on both the system size and connection density. Starting with a small scale system, the correctness of the theoretical results and the superiority in comparison to traditional indexes are verified. Further, we present the quantitative results by means of error analysis, distribution comparison of various indexes and relationship with system structure exploration, and give the position of the key oscillator. The results demonstrate a negligible error between the theoretical and numerical outcomes, and highlighting that the distribution of dynamic survivability centrality closely resembles the distribution of system state changes. The conclusions serve as evidence for the accuracy and validity of the proposed index. The findings provide an effective approach to protect systems to improve dynamic survivability.