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.

中文翻译：

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复杂系统脆弱性的动态进化元模型分析

由于复杂系统的崩溃可能会带来严重后果，因此漏洞通常被视为复杂系统的核心问题。多层网络是分析复杂系统的强大工具，但是复杂网络可能不是模拟子系统的最佳选择。在这项工作中，在多层网络的框架内提出了一个蜂窝图（CG）模型，以分析复杂系统的脆弱性。具体来说，细胞自动机在微观水平上被视为基于动态图的模型的顶点，它们的链接由宏观水平上由随机模型控制的图边缘建模。引入马尔可夫链来说明基于图的模型的演化，并通过低成本推断获得漏洞演化的详细信息。实践证明，这种CG模型可以精确地描述复杂的系统。CG模型由两个实际的组织系统实现，分别用于代表典型的平面结构和典型的金字塔结构。计算结果表明，金字塔结构最初更坚固，而扁平结构在遭受多发打击时最终表现优于金字塔。最后，敏感性分析结果验证并增强了结论的可靠性。