{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T14:22:08Z","timestamp":1781533328521,"version":"3.54.5"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2015,11,27]],"date-time":"2015-11-27T00:00:00Z","timestamp":1448582400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2015,11,27]],"date-time":"2015-11-27T00:00:00Z","timestamp":1448582400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We investigate the emergence of extreme events in interdependent networks. We introduce an inter-layer traffic resource competing mechanism to account for the limited capacity associated with distinct network layers. A striking finding is that, when the number of network layers and\/or the overlap among the layers are increased, extreme events can emerge in a cascading manner on a global scale. Asymptotically, there are two stable absorption states: a state free of extreme events and a state of full of extreme events and the transition between them is abrupt. Our results indicate that internal interactions in the multiplex system can yield qualitatively distinct phenomena associated with extreme events that do not occur for independent network layers. An implication is that, e.g., public resource competitions among different service providers can lead to a higher resource requirement than naively expected. We derive an analytical theory to understand the emergence of global-scale extreme events based on the concept of effective betweenness. We also articulate a cost-effective control scheme through increasing the capacity of very few hubs to suppress the cascading process of extreme events so as to protect the entire multi-layer infrastructure against global-scale breakdown.<\/jats:p>","DOI":"10.1038\/srep17277","type":"journal-article","created":{"date-parts":[[2015,11,27]],"date-time":"2015-11-27T10:24:00Z","timestamp":1448619840000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":36,"title":["Extreme events in multilayer, interdependent complex networks and control"],"prefix":"10.1038","volume":"5","author":[{"given":"Yu-Zhong","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zi-Gang","family":"Huang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hai-Feng","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel","family":"Eisenberg","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thomas P.","family":"Seager","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ying-Cheng","family":"Lai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2015,11,27]]},"reference":[{"key":"BFsrep17277_CR1","doi-asserted-by":"publisher","first-page":"218702","DOI":"10.1103\/PhysRevLett.96.218702","volume":"96","author":"J Duch","year":"2006","unstructured":"Duch, J. & Arenas, A. Scaling of fluctuations in traffic on complex networks. Phys. Rev. Lett. 96, 218702 (2006).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep17277_CR2","doi-asserted-by":"publisher","first-page":"056104","DOI":"10.1103\/PhysRevE.76.056104","volume":"76","author":"S Yoon","year":"2007","unstructured":"Yoon, S., Yook, S.-H. & Kim, Y. Scaling property of flux fluctuations from random walks. Phys. Rev. E 76, 056104 (2007).","journal-title":"Phys. Rev. E"},{"key":"BFsrep17277_CR3","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1088\/1367-2630\/9\/5\/154","volume":"9","author":"B Kujawski","year":"2007","unstructured":"Kujawski, B., Tadi\u0107, B. & Rodgers, G. J. Preferential behaviour and scaling in diffusive dynamics on networks. New. J. Phys. 9, 154 (2007).","journal-title":"New. J. Phys."},{"key":"BFsrep17277_CR4","doi-asserted-by":"publisher","first-page":"208701","DOI":"10.1103\/PhysRevLett.100.208701","volume":"100","author":"S Meloni","year":"2008","unstructured":"Meloni, S., Omez Garde\u00f1es, J. G., Latora, V. & Moreno, Y. Scaling breakdown in flow fluctuations on complex networks. Phys. Rev. Lett. 100, 208701 (2008).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep17277_CR5","doi-asserted-by":"publisher","first-page":"012808","DOI":"10.1103\/PhysRevE.87.012808","volume":"87","author":"Z Zhou","year":"2013","unstructured":"Zhou, Z. et al. Universality of flux-fluctuation law in complex dynamical systems. Phys. Rev. E 87, 012808 (2013).","journal-title":"Phys. Rev. E"},{"key":"BFsrep17277_CR6","doi-asserted-by":"publisher","first-page":"6787","DOI":"10.1038\/srep06787","volume":"4","author":"Z-G Huang","year":"2014","unstructured":"Huang, Z.-G., Dong, J.-Q., Huang, L. & Lai, Y.-C. Universal flux-fluctuation law in small systems. Sci. Rep. 4, 6787 (2014).","journal-title":"Sci. Rep"},{"key":"BFsrep17277_CR7","doi-asserted-by":"publisher","first-page":"188701","DOI":"10.1103\/PhysRevLett.106.188701","volume":"106","author":"V Kishore","year":"2011","unstructured":"Kishore, V., Santhanam, M. S. & Amritkar, R. E. Extreme events on complex networks. Phys. Rev. Lett. 106, 188701 (2011).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep17277_CR8","doi-asserted-by":"publisher","first-page":"056120","DOI":"10.1103\/PhysRevE.85.056120","volume":"85","author":"V Kishore","year":"2012","unstructured":"Kishore, V., Santhanam, M. S. & Amritkar, R. E. Extreme events and event size fluctuations in biased random walks on networks. Phys. Rev. E 85, 056120 (2012).","journal-title":"Phys. Rev. E"},{"key":"BFsrep17277_CR9","doi-asserted-by":"publisher","first-page":"014801","DOI":"10.1103\/PhysRevE.88.014801","volume":"88","author":"V Kishore","year":"2013","unstructured":"Kishore, V., Sonawane, A. R. & Santhanam, M. S. Manipulation of extreme events on scale-free networks. Phys. Rev. E 88, 014801 (2013).","journal-title":"Phys. Rev. E"},{"key":"BFsrep17277_CR10","doi-asserted-by":"publisher","first-page":"6121","DOI":"10.1038\/srep06121","volume":"4","author":"Y-Z Chen","year":"2014","unstructured":"Chen, Y.-Z., Huang, Z.-G. & Lai, Y.-C. Controlling extreme events on complex networks. Sci. Rep. 4, 6121 (2014).","journal-title":"Sci. Rep"},{"key":"BFsrep17277_CR11","doi-asserted-by":"publisher","first-page":"984","DOI":"10.1038\/464984a","volume":"464","author":"A Vespignani","year":"2010","unstructured":"Vespignani, A. Complex networks: The fragility of interdependency. Nature 464, 984\u2013985 (2010).","journal-title":"Nature"},{"key":"BFsrep17277_CR12","doi-asserted-by":"publisher","first-page":"1025","DOI":"10.1038\/nature08932","volume":"464","author":"SV Buldyrev","year":"2010","unstructured":"Buldyrev, S. V., Parshani, R., Paul, G., Stanley, H. E. & Havlin, S. Catastrophic cascade of failures in interdependent networks. Nature 464, 1025\u20131028 (2010).","journal-title":"Nature"},{"key":"BFsrep17277_CR13","doi-asserted-by":"publisher","first-page":"68002","DOI":"10.1209\/0295-5075\/92\/68002","volume":"92","author":"R Parshani","year":"2010","unstructured":"Parshani, R., Rozenblat, C., Ietri, D., Ducruet, C. & Havlin, S. Inter-similarity between coupled networks. Europhys. Lett. 92, 68002 (2010).","journal-title":"Europhys. Lett."},{"key":"BFsrep17277_CR14","doi-asserted-by":"publisher","first-page":"066134","DOI":"10.1103\/PhysRevE.85.066134","volume":"85","author":"J Gao","year":"2012","unstructured":"Gao, J., Buldyrev, S., Havlin, S. & Stanley, H. Robustness of a network formed by n interdependent networks with a one-to-one correspondence of dependent nodes. Phys. Rev. E 85, 066134 (2012).","journal-title":"Phys. Rev. E"},{"key":"BFsrep17277_CR15","doi-asserted-by":"publisher","first-page":"248701","DOI":"10.1103\/PhysRevLett.109.248701","volume":"109","author":"G Baxter","year":"2012","unstructured":"Baxter, G., Dorogovtsev, S., Goltsev, A. & Mendes, J. Avalanche collapse of interdependent networks. Phys. Rev. Lett. 109, 248701 (2012).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep17277_CR16","doi-asserted-by":"publisher","first-page":"036103","DOI":"10.1103\/PhysRevE.86.036103","volume":"86","author":"O Ya\u011fan","year":"2012","unstructured":"Ya\u011fan, O. & Gligor, V. Analysis of complex contagions in random multiplex networks. Phys. Rev. E 86, 036103 (2012).","journal-title":"Phys. Rev. E"},{"key":"BFsrep17277_CR17","doi-asserted-by":"publisher","first-page":"058702","DOI":"10.1103\/PhysRevLett.111.058702","volume":"111","author":"JY Kim","year":"2013","unstructured":"Kim, J. Y. & Goh, K.-T. Coevolution and correlated multiplexity in multiplex networks. Phys. Rev. Lett. 111, 058702 (2013).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep17277_CR18","doi-asserted-by":"publisher","first-page":"128703","DOI":"10.1103\/PhysRevLett.109.128703","volume":"109","author":"RG Morris","year":"2012","unstructured":"Morris, R. G. & Barthelemy, M. Transport on coupled spatial networks. Phys. Rev. Lett. 109, 128703 (2012).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep17277_CR19","doi-asserted-by":"publisher","first-page":"028701","DOI":"10.1103\/PhysRevLett.110.028701","volume":"110","author":"S Gomez","year":"2013","unstructured":"Gomez, S. et al. Diffusion dynamics on multiplex networks. Phys. Rev. Lett. 110, 028701 (2013).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep17277_CR20","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1038\/nphys2761","volume":"9","author":"F Radicchi","year":"2013","unstructured":"Radicchi, F. & Arenas, A. Abrupt transition in the structural formation of interconnected networks. Nat. Phys. 9, 717\u2013720 (2013).","journal-title":"Nat. Phys"},{"key":"BFsrep17277_CR21","doi-asserted-by":"publisher","first-page":"032807","DOI":"10.1103\/PhysRevE.88.032807","volume":"88","author":"A Sole-Ribalta","year":"2013","unstructured":"Sole-Ribalta, A. et al. Spectral properties of the laplacian of multiplex networks. Phys. Rev. E 88, 032807 (2013).","journal-title":"Phys. Rev. E"},{"key":"BFsrep17277_CR22","doi-asserted-by":"publisher","first-page":"5097","DOI":"10.1038\/srep05097","volume":"4","author":"W Wang","year":"2014","unstructured":"Wang, W. et al. Asymmetrically interacting spreading dynamics on complex layered networks. Sci. Rep. 4, 5097 (2014).","journal-title":"Sci. Rep"},{"key":"BFsrep17277_CR23","doi-asserted-by":"publisher","first-page":"056113","DOI":"10.1103\/PhysRevE.86.056113","volume":"86","author":"J G\u00f3mez-Garde\u00f1es","year":"2012","unstructured":"G\u00f3mez-Garde\u00f1es, J., Gracia-L\u00e1zaro, C., Flora, L. M. & Moreno, Y. Evolutionary dynamics on interdependent populations. Phys. Rev. E 86, 056113 (2012).","journal-title":"Phys. Rev. E"},{"key":"BFsrep17277_CR24","doi-asserted-by":"publisher","first-page":"2483","DOI":"10.1038\/srep02483","volume":"3","author":"L-L Jiang","year":"2013","unstructured":"Jiang, L.-L. & Perc, M. Spreading of cooperative behaviour across interdependent groups. Sci. Rep. 3, 2483 (2013).","journal-title":"Sci. Rep."},{"key":"BFsrep17277_CR25","doi-asserted-by":"publisher","first-page":"4436","DOI":"10.1038\/srep04436","volume":"4","author":"M Santos","year":"2014","unstructured":"Santos, M., Dorogovtsev, S. & Mendes, J. Biased imitation in coupled evolutionary games in interdependent networks. Sci. Rep. 4, 4436 (2014).","journal-title":"Sci. Rep"},{"key":"BFsrep17277_CR26","doi-asserted-by":"publisher","first-page":"620","DOI":"10.1038\/srep00620","volume":"2","author":"J G\u00f3mez-Garde\u00f1es","year":"2012","unstructured":"G\u00f3mez-Garde\u00f1es, J., Reinares, I., Arenas, A. & Flora, L. M. Evolution of cooperation in multiplex networks. Sci. Rep. 2, 620 (2012).","journal-title":"Sci. Rep"},{"key":"BFsrep17277_CR27","doi-asserted-by":"publisher","first-page":"056102","DOI":"10.1103\/PhysRevE.86.056102","volume":"86","author":"D Irving","year":"2012","unstructured":"Irving, D. & Sorrentino, F. Synchronization of dynamical hypernetworks: Dimensionality reduction through simultaneous block-diagonalization of matrices. Phys. Rev. E 86, 056102 (2012).","journal-title":"Phys. Rev. E"},{"key":"BFsrep17277_CR28","doi-asserted-by":"publisher","first-page":"033035","DOI":"10.1088\/1367-2630\/14\/3\/033035","volume":"14","author":"F Sorrentino","year":"2012","unstructured":"Sorrentino, F. Synchronization of hypernetworks of coupled dynamical systems. New J. Phys. 14, 033035 (2012).","journal-title":"New J. Phys."},{"key":"BFsrep17277_CR29","doi-asserted-by":"crossref","unstructured":"Aguirre, J., Sevilla-Escoboza, R., Guti\u00e9rrez, R., Papo, D. & Buld\u00fa, J. Synchronization of interconnected networks: the role of connector nodes. arXiv:1406.0081 (2014).","DOI":"10.1103\/PhysRevLett.112.248701"},{"key":"BFsrep17277_CR30","doi-asserted-by":"publisher","first-page":"3289","DOI":"10.1038\/srep03289","volume":"3","author":"V Louzada","year":"2013","unstructured":"Louzada, V., Ara\u00fajo, N., Andrade Jr, J. & Herrmann, H. Breathing synchronization in interconnected networks. Sci. Rep. 3, 3289 (2013).","journal-title":"Sci. Rep"},{"key":"BFsrep17277_CR31","doi-asserted-by":"publisher","first-page":"278701","DOI":"10.1103\/PhysRevLett.87.278701","volume":"87","author":"K-I Goh","year":"2001","unstructured":"Goh, K.-I., Kahng, B. & Kim, D. Universal behavior of load distribution in scale-free networks. Phys. Rev. Lett. 87, 278701 (2001).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep17277_CR32","doi-asserted-by":"publisher","first-page":"118701","DOI":"10.1103\/PhysRevLett.92.118701","volume":"92","author":"JD Noh","year":"2004","unstructured":"Noh, J. D. & Rieger, H. Random walks on complex networks. Phys. Rev. Lett. 92, 118701 (2004).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep17277_CR33","doi-asserted-by":"publisher","first-page":"026109","DOI":"10.1103\/PhysRevE.70.026109","volume":"70","author":"K Park","year":"2004","unstructured":"Park, K., Lai, Y.-C. & Ye, N. Characterization of weighted complex networks. Phys. Rev. E 70, 026109 (2004).","journal-title":"Phys. Rev. E"},{"key":"BFsrep17277_CR34","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1126\/science.286.5439.509","volume":"286","author":"A-L Barab\u00e1si","year":"1999","unstructured":"Barab\u00e1si, A.-L. & Albert, R. Emergence of scaling in random networks. Science 286, 509\u2013512 (1999).","journal-title":"Science"}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/srep17277","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/srep17277.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/srep17277.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,5]],"date-time":"2023-01-05T19:49:12Z","timestamp":1672948152000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/srep17277"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,27]]},"references-count":34,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,12,22]]}},"alternative-id":["BFsrep17277"],"URL":"https:\/\/doi.org\/10.1038\/srep17277","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11,27]]},"assertion":[{"value":"8 September 2015","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 October 2015","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 November 2015","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing financial interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"17277"}}