Research on robustness of R&D network under cascading propagation of risk with gray attack information

• We introduce the negative deviation and positive deviation to measure imprecision of gray attack information.
• We propose the critical threshold of resisting risk as the new indicator of robustness of R&D network.
• We establish the cascading propagation model of risk in R&D network.
• We simulate the cascading propagation of risk to analyze robustness of R&D network.
• This work provides a theoretical basis for preventing and controlling cascading propagation of risk in R&D network.

Facing the cascading propagation phenomenon of risk in R&D network and the imprecision of attack information, this paper builds the cascading propagation model of risk with gray attack information. In this model, gray attack information described by node degree is measured by negative and positive deviations, and the critical threshold of resisting risk is also proposed as a new indicator of robustness of R&D network. Then the paper analyzes the robustness of R&D network under cascading propagation of risk with gray attack information through numerical simulation. The results show that R&D network has the strongest robustness under random attack, but has the weakest one under intentional attack; robustness of R&D network increases with the increase of deviation from attack information, which becomes increasingly significant when all enterprises' capacities distribution is heterogeneous; robustness of R&D network under one attack decreases with the increasing heterogeneity of all enterprises' capacities distribution; robustness of R&D network is more sensitive to the negative deviation than to the positive deviation from attack information. This research work will provide a theoretical basis for preventing and controlling cascading propagation in R&D network in the future.