Resilience and Its Thresholds of Scientific Collaboration Network

Scientific collaboration networks are frequently subjected to various unexpected pressures and shocks, which would lead to system performance dropping substantially and even becoming invalid. Resilience is the capability of a scientific collaboration network to maintain its effectiveness in the event of any attack or perturbation against the network. Here, we investigate an effective measurement index for network resilience and try to accurately predict resilience thresholds in advance. Once resilience is close to or lower than the threshold value, risk evaluation, and resilience-based strategies should be immediately adopted to adjust to a range of actions, thereby ensuring that the network endures large perturbations before reaching the bifurcations and risking a transition to undesired states. Quantitative analysis framework for resilience begins with designing a knowledge dissemination model with interactive collaboration item and different types of experimentally mapped networks. Then, a variety of perturbations are imposed on these simulated networks controlled by the constructed model to test network resilience and its thresholds. Limited by the multidimensional parameter space of the system, critical transitions marking the loss of resilience are unpredictable. Inspired by Gao's work, mapping the multi-dimensional equations into a 1-D resilience function, network resilience can be measured by the effective mapping parameter and bifurcation points of resilience can be solved theoretically. We also validate the calculated critical values with numerical simulations. Our findings can help to design optimal principles for dealing with perturbations or intervention strategies for preventing the loss of resilience happening in scientific collaboration networks.