Predicting the cascading failure of dynamical networks based on a new dimension reduction method

Abstract

Many disaster events occurring frequently on the network are usually triggered by some trivial events, which are often difficult to be accurately predicted. One of the main reasons lies in that the behavior and structure of the network are highly coupled together, which is difficult to be analyzed and separated mathematically. With a universal dynamical overload model capturing the interaction between pairs of nodes in networks, various dynamical systems ranging from epidemic process, to birth–death process, biochemical and regulatory dynamics, are mapped into a one-dimension state space, which can help separate the role of the structure and the dynamic mechanism on the system robustness against cascading failure. Moreover, it can help predict the individual behavior in the cascading process. The theoretical solutions match well with the simulation results on Scale-Free and Erdös–Rényi networks for the four dynamical models, showing that even for networks with the same structure, different dynamic mechanisms have different effects on the robustness. Our research can provide ideas for designing more robust networked systems.