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

我们推导出了计算具有强度-度相关性的复杂网络的逾渗阈值和巨组分分数的解析表达式。通过这些表达式，我们确定了一个网络结构，该网络结构由一组弱互连的随机正则图组成，并且显着改善了无标度网络针对目标高度节点攻击的众所周知的脆弱性。我们还研究了具有层次或模块结构的复杂网络上的集体动力学。我们的研究结果包括指导性和有用的结果，如在囚徒困境游戏中，“永久合作者”的连接集群表现出渗透过渡。

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.