Cascading Failures in Interdependent Networks with Multiple Supply-Demand Links and Functionality Thresholds

Di Muro, M. A.; Valdez, L. D.; Aragão Rêgo, H. H.; Buldyrev, S. V.; Stanley, H. E.; Braunstein, L. A.

doi:10.1038/s41598-017-14384-y

Cascading Failures in Interdependent Networks with Multiple Supply-Demand Links and Functionality Thresholds

Journal Article · Tue Nov 07 23:00:00 EST 2017 · Scientific Reports

DOI:https://doi.org/10.1038/s41598-017-14384-y· OSTI ID:1624357

Di Muro, M. A. ^[1]; Valdez, L. D. ^[2]; Aragão Rêgo, H. H. ^[3]; Buldyrev, S. V. ^[4]; Stanley, H. E. ^[5]; Braunstein, L. A. ^[6]

Universidad Nacional de Mar del Plata-CONICET (Argentina); DOE/OSTI
Ciudad Universitaria (Argentina); Universidad Nacional de Córdoba (Argentina)
Ciência e Tecnologia do Maranhão (Brazil)
Yeshiva Univ., New York, NY (United States)
Boston Univ., MA (United States)
Universidad Nacional de Mar del Plata-CONICET (Argentina); Boston Univ., MA (United States)

Various social, financial, biological and technological systems can be modeled by interdependent networks. It has been assumed that in order to remain functional, nodes in one network must receive the support from nodes belonging to different networks. So far these models have been limited to the case in which the failure propagates across networks only if the nodes lose all their supply nodes. In this paper we develop a more realistic model for two interdependent networks in which each node has its own supply threshold, i.e., they need the support of a minimum number of supply nodes to remain functional. In addition, we analyze different conditions of internal node failure due to disconnection from nodes within its own network. We show that several local internal failure conditions lead to similar nontrivial results. When there are no internal failures the model is equivalent to a bipartite system, which can be useful to model a financial market. We explore the rich behaviors of these models that include discontinuous and continuous phase transitions. Using the generating functions formalism, we analytically solve all the models in the limit of infinitely large networks and find an excellent agreement with the stochastic simulations.

View Accepted Manuscript (DOE)

Research Organization:: Idaho National Laboratory (INL), Idaho Falls, ID (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC07-05ID14517

OSTI ID:: 1624357

Journal Information:: Scientific Reports, Journal Name: Scientific Reports Journal Issue: 1 Vol. 7; ISSN 2045-2322

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

References (58)

A critical point for random graphs with a given degree sequence Molloy, Michael; Reed, Bruce Random Structures & Algorithms, Vol. 6, Issue 2-3 https://doi.org/10.1002/rsa.3240060204	journal	March 1995
Networks of networks – An introduction Kenett, Dror Y.; Perc, Matjaž; Boccaletti, Stefano Chaos, Solitons & Fractals, Vol. 80 https://doi.org/10.1016/j.chaos.2015.03.016	journal	November 2015
Catastrophic cascade of failures in interdependent networks Buldyrev, Sergey V.; Parshani, Roni; Paul, Gerald Nature, Vol. 464, Issue 7291 https://doi.org/10.1038/nature08932	journal	April 2010
Spatio-temporal propagation of cascading overload failures in spatially embedded networks Zhao, Jichang; Li, Daqing; Sanhedrai, Hillel Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms10094	journal	January 2016
Networks formed from interdependent networks Gao, Jianxi; Buldyrev, Sergey V.; Stanley, H. Eugene Nature Physics, Vol. 8, Issue 1 https://doi.org/10.1038/nphys2180	journal	December 2011
The extreme vulnerability of interdependent spatially embedded networks Bashan, Amir; Berezin, Yehiel; Buldyrev, Sergey V. Nature Physics, Vol. 9, Issue 10 https://doi.org/10.1038/nphys2727	journal	August 2013
Recovery of Interdependent Networks Di Muro, M. A.; La Rocca, C. E.; Stanley, H. E. Scientific Reports, Vol. 6, Issue 1 https://doi.org/10.1038/srep22834	journal	March 2016
A simple model of global cascades on random networks Watts, D. J. Proceedings of the National Academy of Sciences, Vol. 99, Issue 9 https://doi.org/10.1073/pnas.082090499	journal	April 2002
Evolution of networks Dorogovtsev, S. N.; Mendes, J. F. F. Advances in Physics, Vol. 51, Issue 4 https://doi.org/10.1080/00018730110112519	journal	June 2002
A triple point induced by targeted autonomization on interdependent scale-free networks Valdez, L. D.; Macri, P. A.; Braunstein, L. A. Journal of Physics A: Mathematical and Theoretical, Vol. 47, Issue 5 https://doi.org/10.1088/1751-8113/47/5/055002	journal	January 2014
Networks Newman, Mark https://doi.org/10.1093/acprof:oso/9780199206650.001.0001	book	March 2010
The Structure of Complex Networks: Theory and Applications Estrada, Ernesto https://doi.org/10.1093/acprof:oso/9780199591756.001.0001	book	October 2011
Random graphs with arbitrary degree distributions and their applications Newman, M. E. J.; Strogatz, S. H.; Watts, D. J. Physical Review E, Vol. 64, Issue 2 https://doi.org/10.1103/PhysRevE.64.026118	journal	July 2001
Bootstrap percolation on complex networks Baxter, G. J.; Dorogovtsev, S. N.; Goltsev, A. V. Physical Review E, Vol. 82, Issue 1 https://doi.org/10.1103/PhysRevE.82.011103	journal	July 2010
Interdependent networks with identical degrees of mutually dependent nodes Buldyrev, Sergey V.; Shere, Nathaniel W.; Cwilich, Gabriel A. Physical Review E, Vol. 83, Issue 1 https://doi.org/10.1103/PhysRevE.83.016112	journal	January 2011
Cascade of failures in coupled network systems with multiple support-dependence relations Shao, Jia; Buldyrev, Sergey V.; Havlin, Shlomo Physical Review E, Vol. 83, Issue 3 https://doi.org/10.1103/PhysRevE.83.036116	journal	March 2011
Heterogeneous k -core versus bootstrap percolation on complex networks Baxter, G. J.; Dorogovtsev, S. N.; Goltsev, A. V. Physical Review E, Vol. 83, Issue 5 https://doi.org/10.1103/PhysRevE.83.051134	journal	May 2011
Robustness of interdependent networks under targeted attack Huang, Xuqing; Gao, Jianxi; Buldyrev, Sergey V. Physical Review E, Vol. 83, Issue 6 https://doi.org/10.1103/PhysRevE.83.065101	journal	June 2011
Robustness of onionlike correlated networks against targeted attacks Tanizawa, Toshihiro; Havlin, Shlomo; Stanley, H. Eugene Physical Review E, Vol. 85, Issue 4 https://doi.org/10.1103/PhysRevE.85.046109	journal	April 2012
Robustness of a network formed by n interdependent networks with a one-to-one correspondence of dependent nodes Gao, Jianxi; Buldyrev, S. V.; Havlin, S. Physical Review E, Vol. 85, Issue 6 https://doi.org/10.1103/PhysRevE.85.066134	journal	June 2012
Critical phenomena in heterogeneous k -core percolation Cellai, Davide; Lawlor, Aonghus; Dawson, Kenneth A. Physical Review E, Vol. 87, Issue 2 https://doi.org/10.1103/PhysRevE.87.022134	journal	February 2013
Robustness of network of networks under targeted attack Dong, Gaogao; Gao, Jianxi; Du, Ruijin Physical Review E, Vol. 87, Issue 5 https://doi.org/10.1103/PhysRevE.87.052804	journal	May 2013
Triple point in correlated interdependent networks Valdez, L. D.; Macri, P. A.; Stanley, H. E. Physical Review E, Vol. 88, Issue 5 https://doi.org/10.1103/PhysRevE.88.050803	journal	November 2013
Percolation of a general network of networks Gao, Jianxi; Buldyrev, Sergey V.; Stanley, H. Eugene Physical Review E, Vol. 88, Issue 6 https://doi.org/10.1103/PhysRevE.88.062816	journal	December 2013
Multiple percolation transitions in a configuration model of a network of networks Bianconi, Ginestra; Dorogovtsev, Sergey N. Physical Review E, Vol. 89, Issue 6 https://doi.org/10.1103/PhysRevE.89.062814	journal	June 2014
k -core percolation on complex networks: Comparing random, localized, and targeted attacks Yuan, Xin; Dai, Yang; Stanley, H. Eugene Physical Review E, Vol. 93, Issue 6 https://doi.org/10.1103/PhysRevE.93.062302	journal	June 2016
Cascading failures in interdependent networks with finite functional components Di Muro, M. A.; Buldyrev, S. V.; Stanley, H. E. Physical Review E, Vol. 94, Issue 4 https://doi.org/10.1103/PhysRevE.94.042304	journal	October 2016
Interdependent Networks: Reducing the Coupling Strength Leads to a Change from a First to Second Order Percolation Transition Parshani, Roni; Buldyrev, Sergey V.; Havlin, Shlomo Physical Review Letters, Vol. 105, Issue 4 https://doi.org/10.1103/PhysRevLett.105.048701	journal	July 2010
Robustness of a Network of Networks Gao, Jianxi; Buldyrev, Sergey V.; Havlin, Shlomo Physical Review Letters, Vol. 107, Issue 19 https://doi.org/10.1103/PhysRevLett.107.195701	journal	November 2011
Cascading Failures in Interdependent Lattice Networks: The Critical Role of the Length of Dependency Links Li, Wei; Bashan, Amir; Buldyrev, Sergey V. Physical Review Letters, Vol. 108, Issue 22 https://doi.org/10.1103/PhysRevLett.108.228702	journal	May 2012
Avalanche Collapse of Interdependent Networks Baxter, G. J.; Dorogovtsev, S. N.; Goltsev, A. V. Physical Review Letters, Vol. 109, Issue 24 https://doi.org/10.1103/PhysRevLett.109.248701	journal	December 2012
Network Robustness and Fragility: Percolation on Random Graphs Callaway, Duncan S.; Newman, M. E. J.; Strogatz, Steven H. Physical Review Letters, Vol. 85, Issue 25 https://doi.org/10.1103/PhysRevLett.85.5468	journal	December 2000
Critical phenomena in complex networks Dorogovtsev, S. N.; Goltsev, A. V.; Mendes, J. F. F. Reviews of Modern Physics, Vol. 80, Issue 4 https://doi.org/10.1103/RevModPhys.80.1275	journal	October 2008
Identifying, understanding, and analyzing critical infrastructure interdependencies Rinaldi, S. M.; Peerenboom, J. P.; Kelly, T. K. IEEE Control Systems, Vol. 21, Issue 6, p. 11-25 https://doi.org/10.1109/37.969131	journal	December 2001
Optimal Allocation of Interconnecting Links in Cyber-Physical Systems: Interdependence, Cascading Failures, and Robustness Yagan, Osman; Qian, Dajun; Zhang, Junshan IEEE Transactions on Parallel and Distributed Systems, Vol. 23, Issue 9 https://doi.org/10.1109/TPDS.2012.62	journal	September 2012
Evolutionary games on multilayer networks: a colloquium Wang, Zhen; Wang, Lin; Szolnoki, Attila The European Physical Journal B, Vol. 88, Issue 5 https://doi.org/10.1140/epjb/e2015-60270-7	journal	May 2015
Inter-similarity between coupled networks Parshani, R.; Rozenblat, C.; Ietri, D. EPL (Europhysics Letters), Vol. 92, Issue 6 https://doi.org/10.1209/0295-5075/92/68002	journal	December 2010
Percolation theory on interdependent networks based on epidemic spreading Son, Seung-Woo; Bizhani, Golnoosh; Christensen, Claire EPL (Europhysics Letters), Vol. 97, Issue 1 https://doi.org/10.1209/0295-5075/97/16006	journal	January 2012
Modelling interdependent infrastructures using interacting dynamical models Rosato, V.; Issacharoff, L.; Tiriticco, F. International Journal of Critical Infrastructures, Vol. 4, Issue 1/2 https://doi.org/10.1504/IJCIS.2008.016092	journal	January 2008
A simple model of global cascades on random networks Watts, Duncan J. The Structure and Dynamics of Networks https://doi.org/10.1515/9781400841356.497	book	January 2006
Catastrophic cascade of failures in interdependent networks Buldyrev, Sergey V.; Parshani, Roni; Paul, Gerald arXiv https://doi.org/10.48550/arxiv.0907.1182	text	January 2009
Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition Parshani, Roni; Buldyrev, Sergey V.; Havlin, Shlomo arXiv https://doi.org/10.48550/arxiv.1004.3989	text	January 2010
Robustness of interdependent networks under targeted attack Huang, Xuqing; Gao, Jianxi; Buldyrev, Sergey V. arXiv https://doi.org/10.48550/arxiv.1010.2160	text	January 2010
Inter-similarity between coupled networks Parshani, Roni; Rozenblat, Celine; Ietri, Daniele arXiv https://doi.org/10.48550/arxiv.1010.4506	text	January 2010
Robustness of a Network of Networks Gao, Jianxi; Buldyrev, Sergey V.; Havlin, Shlomo arXiv https://doi.org/10.48550/arxiv.1010.5829	text	January 2010
Heterogeneous-k-core versus Bootstrap Percolation on Complex Networks Baxter, G. J.; Dorogovtsev, S. N.; Goltsev, A. V. arXiv https://doi.org/10.48550/arxiv.1012.4336	text	January 2010
Robustness of onion-like correlated networks against targeted attacks Tanizawa, Toshihiro; Havlin, Shlomo; Stanley, H. Eugene arXiv https://doi.org/10.48550/arxiv.1112.5297	text	January 2011
Cascading Failures in Interdependent Lattice Networks: The Critical Role of the Length of Dependency Links Li, Wei; Bashan, Amir; Buldyrev, Sergey V. arXiv https://doi.org/10.48550/arxiv.1206.0224	preprint	January 2012
The extreme vulnerability of interdependent spatially embedded networks Bashan, Amir; Berezin, Yehiel; Buldyrev, Sergey V. arXiv https://doi.org/10.48550/arxiv.1206.2062	text	January 2012
Critical phenomena in heterogeneous k-core percolation Cellai, Davide; Lawlor, Aonghus; Dawson, Kenneth A. arXiv https://doi.org/10.48550/arxiv.1209.2928	text	January 2012
Percolation of a general network of networks Gao, Jianxi; Buldyrev, Sergey V.; Stanley, H. Eugene arXiv https://doi.org/10.48550/arxiv.1306.3416	text	January 2013
Triple Point in Correlated Interdependent Networks Valdez, L. D.; Macri, P. A.; Stanley, H. E. arXiv https://doi.org/10.48550/arxiv.1308.4216	text	January 2013
Triple point induced by targeted autonomization on interdependent scale free networks Valdez, L. D.; Macri, P. A.; Braunstein, L. A. arXiv https://doi.org/10.48550/arxiv.1310.6345	text	January 2013
Evolutionary games on multilayer networks: A colloquium Wang, Zhen; Wang, Lin; Szolnoki, Attila arXiv https://doi.org/10.48550/arxiv.1504.04359	text	January 2015
Recovery of Interdependent Networks Di Muro, M. A.; La Rocca, C. E.; Stanley, H. E. arXiv https://doi.org/10.48550/arxiv.1512.02555	preprint	January 2015
$k$-core percolation on complex networks: Comparing random, localized and targeted attacks Yuan, Xin; Dai, Yang; Stanley, H. Eugene arXiv https://doi.org/10.48550/arxiv.1605.06386	text	January 2016
Random graphs with arbitrary degree distributions and their applications Newman, M. E. J.; Strogatz, S. H.; Watts, D. J. arXiv https://doi.org/10.48550/arxiv.cond-mat/0007235	text	January 2000
Network robustness and fragility: Percolation on random graphs Callaway, D. S.; Newman, M. E. J.; Strogatz, S. H. arXiv https://doi.org/10.48550/arxiv.cond-mat/0007300	text	January 2000

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