%0 Journal Article %1 Li2012Cascading %A Li, Wei %A Bashan, Amir %A Buldyrev, Sergey V. %A Stanley, H. Eugene %A Havlin, Shlomo %D 2012 %I American Physical Society %J Phys. Rev. Lett. %K spatial-networks percolation critical-phenomena lattice-models interdependent-networks %P 228702+ %R 10.1103/physrevlett.108.228702 %T Cascading Failures in Interdependent Lattice Networks: The Critical Role of the Length of Dependency Links %U http://dx.doi.org/10.1103/physrevlett.108.228702 %V 108 %X We study the cascading failures in a system composed of two interdependent square lattice networks \$A\$ and \$B\$ placed on the same Cartesian plane, where each node in network \$A\$ depends on a node in network \$B\$ randomly chosen within a certain distance \$r\$ from the corresponding node in network \$A\$ and vice versa. Our results suggest that percolation for small \$r\$ below \$r\_max\approx8\$ (lattice units) is a second-order transition, and for larger \$r\$ is a first-order transition. For \$r<r\_max\$, the critical threshold increases linearly with \$r\$ from 0.593 at \$r=0\$ and reaches a maximum, 0.738 for \$r=r\_max\$, and then gradually decreases to 0.683 for \$r=ınfty\$. Our analytical considerations are in good agreement with simulations. Our study suggests that interdependent infrastructures embedded in Euclidean space become most vulnerable when the distance between interdependent nodes is in the intermediate range, which is much smaller than the size of the system.

@article{Li2012Cascading, abstract = {We study the cascading failures in a system composed of two interdependent square lattice networks \$A\$ and \$B\$ placed on the same Cartesian plane, where each node in network \$A\$ depends on a node in network \$B\$ randomly chosen within a certain distance \$r\$ from the corresponding node in network \$A\$ and vice versa. Our results suggest that percolation for small \$r\$ below \${r}\_{\mathrm{max}}\ensuremath{\approx}8\$ (lattice units) is a second-order transition, and for larger \$r\$ is a first-order transition. For \$r\<{r}\_{\mathrm{max}}\$, the critical threshold increases linearly with \$r\$ from 0.593 at \$r=0\$ and reaches a maximum, 0.738 for \$r={r}\_{\mathrm{max}}\$, and then gradually decreases to 0.683 for \$r=\ensuremath{\infty}\$. Our analytical considerations are in good agreement with simulations. Our study suggests that interdependent infrastructures embedded in Euclidean space become most vulnerable when the distance between interdependent nodes is in the intermediate range, which is much smaller than the size of the system.}, added-at = {2019-06-10T14:53:09.000+0200}, author = {Li, Wei and Bashan, Amir and Buldyrev, Sergey V. and Stanley, H. Eugene and Havlin, Shlomo}, biburl = {https://www.bibsonomy.org/bibtex/253451574c39583d4ecc64510443236fd/nonancourt}, citeulike-article-id = {10722692}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/physrevlett.108.228702}, citeulike-linkout-1 = {http://link.aps.org/abstract/PRL/v108/i22/e228702}, citeulike-linkout-2 = {http://link.aps.org/pdf/PRL/v108/i22/e228702}, doi = {10.1103/physrevlett.108.228702}, interhash = {aeab377dbca679c7eafb153ed4702d6e}, intrahash = {53451574c39583d4ecc64510443236fd}, journal = {Phys. Rev. Lett.}, keywords = {spatial-networks percolation critical-phenomena lattice-models interdependent-networks}, month = may, pages = {228702+}, posted-at = {2012-05-31 17:49:13}, priority = {2}, publisher = {American Physical Society}, timestamp = {2019-08-01T15:38:00.000+0200}, title = {{Cascading Failures in Interdependent Lattice Networks: The Critical Role of the Length of Dependency Links}}, url = {http://dx.doi.org/10.1103/physrevlett.108.228702}, volume = 108, year = 2012 }