%0 Journal Article %1 Zhou2013Percolation %A Zhou, Di %A Gao, Jianxi %A Stanley, H. Eugene %A Havlin, Shlomo %D 2013 %J Physical Review E %K hybrid-transitions, percolation interdependent-networks scale-free-networks %N 5 %R 10.1103/PhysRevE.87.052812 %T Percolation of partially interdependent scale-free networks %U http://dx.doi.org/10.1103/PhysRevE.87.052812 %V 87 %X The phase behaviors of two interdependent scale-free (SF) networks under random attack of removing \$1-p\$ fraction of nodes are rich and interesting. Only when the coupling strength \$q=1\$ the percolation phase transition is a first order transition. When \$q\$ is less than 1, at the end stage of the cascade failure, the SF networks will always survive and a non-zero giant cluster \$P\_ınfty\$ will always exist, thus the theoretical critical point \$p\_c\$ goes to \$zero\$. However, a hybrid transition will be observed at the \$1>q>0\$ region, where as \$q\$ descends gradually, the phase transition of \$P\_ınfty\$ will undergoes from quasi-first-order transition, to mix-order transition, then to a quasi-second-order transition, and eventually becomes a real second order transition at \$q=0\$.

@article{Zhou2013Percolation, abstract = {{The phase behaviors of two interdependent scale-free (SF) networks under random attack of removing \$1-p\$ fraction of nodes are rich and interesting. Only when the coupling strength \$q=1\$ the percolation phase transition is a first order transition. When \$q\$ is less than 1, at the end stage of the cascade failure, the SF networks will always survive and a non-zero giant cluster \$P\_\infty\$ will always exist, thus the theoretical critical point \$p\_c\$ goes to \$zero\$. However, a hybrid transition will be observed at the \$1>q>0\$ region, where as \$q\$ descends gradually, the phase transition of \$P\_\infty\$ will undergoes from quasi-first-order transition, to mix-order transition, then to a quasi-second-order transition, and eventually becomes a real second order transition at \$q=0\$.}}, added-at = {2019-06-10T14:53:09.000+0200}, archiveprefix = {arXiv}, author = {Zhou, Di and Gao, Jianxi and Stanley, H. Eugene and Havlin, Shlomo}, biburl = {https://www.bibsonomy.org/bibtex/2f2ba68adf3de28e582916083890e697d/nonancourt}, citeulike-article-id = {10786549}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRevE.87.052812}, citeulike-linkout-1 = {http://arxiv.org/abs/1206.2427}, citeulike-linkout-2 = {http://arxiv.org/pdf/1206.2427}, day = 12, doi = {10.1103/PhysRevE.87.052812}, eprint = {1206.2427}, interhash = {17aba9b6d489ad83fb51b37353cd696b}, intrahash = {f2ba68adf3de28e582916083890e697d}, issn = {1550-2376}, journal = {Physical Review E}, keywords = {hybrid-transitions, percolation interdependent-networks scale-free-networks}, month = may, number = 5, posted-at = {2012-06-13 14:26:43}, priority = {2}, timestamp = {2019-08-01T16:13:01.000+0200}, title = {{Percolation of partially interdependent scale-free networks}}, url = {http://dx.doi.org/10.1103/PhysRevE.87.052812}, volume = 87, year = 2013 }