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Percolation on coupled networks with multiple effective dependency links. (English) Zbl 1462.90026

Summary: The ubiquitous coupled relationship between network systems has become an essential paradigm to depict complex systems. A remarkable property in the coupled complex systems is that a functional node should have multiple external support associations in addition to maintaining the connectivity of the local network. In this paper, we develop a theoretical framework to study the structural robustness of the coupled network with multiple useful dependency links. It is defined that a functional node has the broadest connectivity within the internal network and requires at least \(M\) support link of the other network to function. In this model, we present exact analytical expressions for the process of cascading failures, the fraction of functional nodes in the stable state, and provide a calculation method of the critical threshold. The results indicate that the system undergoes an abrupt phase transition behavior after initial failure. Moreover, the minimum inner and inter-connectivity density to maintain system survival is graphically presented at different multiple effective dependency links. Furthermore, we find that the system needs more internal connection densities to avoid collapse when it requires more effective support links. These findings allow us to reveal the details of a more realistic coupled complex system and develop efficient approaches for designing resilient infrastructure.
©2021 American Institute of Physics

MSC:

90B10 Deterministic network models in operations research
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[1] Shekhtman, L. M.; Danziger, M. M.; Havlin, S., Recent advances on failure and recovery in networks of networks, Chaos, Solitons Fractals, 90, 28-36 (2016) · Zbl 1360.90005
[2] Gao, J.; Buldyrev, S. V.; Eugene Stanley, H.; Havlin, S., Networks formed from interdependent networks, Nat. Phys., 8, 1, 40-48 (2012)
[3] Newman, M. E. J., The structure and function of complex networks, SIAM Rev., 45, 2, 167-256 (2003) · Zbl 1029.68010
[4] Albert, R.; Barabási, A.-L., Statistical mechanics of complex networks, Rev. Mod. Phys., 74, 1, 47 (2002) · Zbl 1205.82086
[5] Watts, D. J.; Strogatz, S. H., Collective dynamics of ‘small-world’ networks, Nature, 393, 6684, 440-442 (1998) · Zbl 1368.05139
[6] Cohen, R.; Havlin, S., Complex Networks: Structure, Robustness and Function (2010), Cambridge University Press · Zbl 1196.05092
[7] Perc, M.; Jordan, J. J.; Rand, D. G.; Wang, Z.; Boccaletti, S.; Szolnoki, A., Statistical physics of human cooperation, Phys. Rep., 687, 1-51 (2017) · Zbl 1366.80006
[8] Liu, Y.; Sanhedrai, H.; Dong, G.; Shekhtman, L. M.; Wang, F.; Buldyrev, S. V.; Havlin, S., Efficient network immunization under limited knowledge, Nat. Sci. Rev., 8, nwaa229 (2021)
[9] Havlin, S.; Eugene Stanley, H.; Bashan, A.; Gao, J.; Kenett, D. Y., Percolation of interdependent network of networks, Chaos, Solitons Fractals, 72, 4-19 (2015) · Zbl 1352.90019
[10] Wang, Z.; Szolnoki, A.; Perc, M., Interdependent network reciprocity in evolutionary games, Sci. Rep., 3, 1183 (2013)
[11] Buldyrev, S. V.; Parshani, R.; Paul, G.; Eugene Stanley, H.; Havlin, S., Catastrophic cascade of failures in interdependent networks, Nature, 464, 7291, 1025-1028 (2010)
[12] Goldstein, P.; Weissman-Fogel, I.; Dumas, G.; Shamay-Tsoory, S. G., Brain-to-brain coupling during handholding is associated with pain reduction, Proc. Natl. Acad. Sci. U.S.A., 115, 11, E2528-E2537 (2018)
[13] Hellmann, F.; Schultz, P.; Jaros, P.; Levchenko, R.; Kapitaniak, T.; Kurths, J.; Maistrenko, Y., Network-induced multistability through lossy coupling and exotic solitary states, Nat. Commun., 11, 1, 1-9 (2020)
[14] Liu, X.; Eugene Stanley, H.; Gao, J., Breakdown of interdependent directed networks, Proc. Natl. Acad. Sci. U.S.A., 113, 5, 1138-1143 (2016)
[15] Dong, G.; Gao, J.; Du, R.; Tian, L.; Eugene Stanley, H.; Havlin, S., Robustness of network of networks under targeted attack, Phys. Rev. E, 87, 5, 052804 (2013)
[16] Zou, Y.; Donner, R. V.; Marwan, N.; Donges, J. F.; Kurths, J., Complex network approaches to nonlinear time series analysis, Phys. Rep., 787, 1-97 (2019)
[17] Lambiotte, R.; Rosvall, M.; Scholtes, I., From networks to optimal higher-order models of complex systems, Nat. Phys., 15, 4, 313-320 (2019)
[18] Bianconi, G., Multilayer Networks: Structure and Function (2018), Oxford University Press
[19] Schäfer, B.; Witthaut, D.; Timme, M.; Latora, V., Dynamically induced cascading failures in power grids, Nat. Commun., 9, 1, 1-13 (2018)
[20] Gao, J.; Buldyrev, S. V.; Havlin, S.; Eugene Stanley, H., Robustness of a network of networks, Phys. Rev. Lett., 107, 19, 195701 (2011)
[21] Dong, G.; Gao, J.; Tian, L.; Du, R.; He, Y., Percolation of partially interdependent networks under targeted attack, Phys. Rev. E, 85, 1, 016112 (2012)
[22] Zhang, H.; Zhou, J.; Zou, Y.; Tang, M.; Xiao, G.; Eugene Stanley, H., Asymmetric interdependent networks with multiple-dependence relation, Phys. Rev. E, 101, 2, 022314 (2020)
[23] Leicht, E. A.; D’Souza, R. M.
[24] Szell, M.; Lambiotte, R.; Thurner, S., Multirelational organization of large-scale social networks in an online world, Proc. Natl. Acad. Sci. U.S.A., 107, 31, 13636-13641 (2010)
[25] Dong, G.; Fan, J.; Shekhtman, L. M.; Shai, S.; Du, R.; Tian, L.; Chen, X.; Eugene Stanley, H.; Havlin, S., Resilience of networks with community structure behaves as if under an external field, Proc. Natl. Acad. Sci. U.S.A., 115, 27, 6911-6915 (2018)
[26] Hu, Y.; Ksherim, B.; Cohen, R.; Havlin, S., Percolation in interdependent and interconnected networks: Abrupt change from second- to first-order transitions, Phys. Rev. E, 84, 6, 066116 (2011)
[27] Reis, S. D. S.; Hu, Y.; Babino, A.; Andrade, J. S. Jr.; Canals, S.; Sigman, M.; Makse, H. A., Avoiding catastrophic failure in correlated networks of networks, Nat. Phys., 10, 10, 762-767 (2014)
[28] Shao, J.; Buldyrev, S. V.; Havlin, S.; Eugene Stanley, H., Cascade of failures in coupled network systems with multiple support-dependence relations, Phys. Rev. E, 83, 3, 036116 (2011)
[29] Dong, G.; Chen, Y.; Wang, F.; Du, R.; Tian, L.; Eugene Stanley, H., Robustness on interdependent networks with a multiple-to-multiple dependent relationship, Chaos, 29, 7, 073107 (2019) · Zbl 1423.90031
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