Xue Leyang, Gao Shengling, Gallos Lazaros K, Levy Orr, Gross Bnaya, Di Zengru, Havlin Shlomo
International Academic Center of Complex Systems, Beijing Normal University, Zhuhai, 519087, China.
School of Systems Science, Beijing Normal University, Beijing, 100875, China.
Nat Commun. 2024 Jul 12;15(1):5850. doi: 10.1038/s41467-024-50273-5.
K-core percolation is a fundamental dynamical process in complex networks with applications that span numerous real-world systems. Earlier studies focus primarily on random networks without spatial constraints and reveal intriguing mixed-order transitions. However, real-world systems, ranging from transportation and communication networks to complex brain networks, are not random but are spatially embedded. Here, we study k-core percolation on two-dimensional spatially embedded networks and show that, in contrast to regular percolation, the length of connections can control the transition type, leading to four different types of phase transitions associated with interesting phenomena and a rich phase diagram. A key finding is the existence of a metastable phase where microscopic localized damage, independent of system size, can cause a macroscopic phase transition, a result which cannot be achieved in traditional percolation. In this case, local failures spontaneously propagate the damage radially until the system collapses, a phenomenon analogous to the nucleation process.
K 核渗流是复杂网络中的一种基本动力学过程，其应用涵盖众多现实世界系统。早期研究主要集中在无空间约束的随机网络上，并揭示了有趣的混合阶跃转变。然而，从交通和通信网络到复杂脑网络等现实世界系统并非随机的，而是空间嵌入的。在此，我们研究二维空间嵌入网络上的 K 核渗流，并表明与常规渗流不同，连接长度可控制转变类型，导致与有趣现象相关的四种不同类型的相变以及丰富的相图。一个关键发现是存在一个亚稳相，其中微观局部损伤（与系统大小无关）可导致宏观相变，这一结果在传统渗流中无法实现。在这种情况下，局部故障会自发地将损伤径向传播，直至系统崩溃，这一现象类似于成核过程。
