Dynamic evolutionary metamodel analysis of the vulnerability of complex systems

Because the collapse of complex systems can have severe consequences, vulnerability is often seen as the core problem of complex systems. Multilayer networks are powerful tools to analyze complex systems, but complex networks may not be the best choice to mimic subsystems. In this work, a cellular graph (CG) model is proposed within the framework of multilayer networks to analyze the vulnerability of complex systems. Specifically, cellular automata are considered the vertices of a dynamic graph-based model at the microlevel, and their links are modeled by graph edges governed by a stochastic model at the macrolevel. A Markov chain is introduced to illustrate the evolution of the graph-based model and to obtain the details of the vulnerability evolution with low-cost inferences. This CG model is proven to describe complex systems precisely. The CG model is implemented with two actual organizational systems, which are used on behalf of the typical flat structure and the typical pyramid structure, respectively. The computational results show that the pyramid structure is initially more robust, while the flat structure eventually outperforms it when being exposed to multiple-rounds strike. Finally, the sensitivity analysis results verify and strengthen the reliability of the conclusions.