The renormalization group approach to coexistence dynamics on complex networks with randomness

针对任意类型的基于度的攻击，我们推导出了具有强度-度相关性的复杂网络的渗流阈值和巨分量分数的计算解析表达式。利用这些表达式，我们确定了一种由一组弱互连随机正则图组成的网络结构，它显著改善了众所周知的无标度网络对目标高度节点攻击的脆弱性。我们还研究了具有层次结构或模块结构的复杂网络的集体动力学。我们的发现包括有指导意义的和有用的结果，即在囚犯困境博弈中，相连的“永久合作者”集群呈现出渗流转变。

We derived the analytical expressions for calculation of the percolation threshold and the giant component fraction of complex networks with strong degree-degree correlation against arbitrary types of degree based attack. With these expressions, we identified a network structure that consists of a set of weakly interconnected random regular graphs and that significantly improves the well-known vulnerability of scale-free networks against targeted high-degree node attack. We also investigated collective dynamics on complex networks with hierarchical or module structure. Our findings include instructive and useful results such that, in the prisoners' dilemma game, the connected cluster of"permanent cooperators"exhibits a percolation transition.