Vulnerability analysis of interdependent R&D networks under risk cascading propagation

Considering that some research and development (R&D) networks are becoming increasingly interdependent, risk not only propagates within one R&D network but also spreads to other R&D networks. This paper proposes a model of risk cascading propagation in order to explore the vulnerability of interdependent R&D networks. Firstly, we propose the generation algorithm of individual R&D networks based on the rules of preferential attachment and geographical proximity, and then build the interdependences between two R&D networks by identifying the input interdependence and shared interdependence. Secondly, we propose the model of risk propagation within one R&D network by defining the risk load and risk capacity of each enterprise, and building the rule of conditional triggering among risks. We then propose the four-stage model for describing the process of risk cascading propagation across interdependent R&D networks. Finally, we investigate the vulnerability of interdependent R&D networks to risk cascading propagation through numerical simulation. Simulation results show that the critical tolerance threshold β∗ can effectively indicate the vulnerability of interdependent R&D networks to risk cascading propagation. When the value of the tolerance parameter β exceeds the critical tolerance threshold β∗, the risk cascading propagation can be entirely prevented in interdependent R&D networks. The vulnerability of interdependent R&D networks increases with the increasing heterogeneity degree of all the enterprises’ risk capacities. The interdependences between interdependent R&D networks can increase their vulnerability to risk cascading propagation. Random attack has the least impact on the vulnerability of interdependent R&D networks, whereas high-degree attack and high-capacity attack have the same impact on the vulnerability.