1 Scientific RepoRts | 5:17277 | DOI: 10.1038/srep17277 www.nature.com/scientificreports extreme events in multilayer, interdependent complex networks and control Yu-Zhong Chen 1 , Zi-Gang Huang 1,2 , Hai-Feng Zhang 3 , Daniel eisenberg 4 , thomas p. seager 4 & Ying-Cheng Lai 1,5 We investigate the emergence of extreme events in interdependent networks. We introduce an inter-layer trafc resource competing mechanism to account for the limited capacity associated with distinct network layers. A striking fnding 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 diferent 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 efective betweenness. We also articulate a cost-efective 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. Internal resource competitions are ubiquitous in complex dynamical systems, but relatively little atten- tion has been paid to its impact on the dynamical evolution and resilience of the underlying interdepend- ent, multilayer networked systems. Relevant situations include the airport and train-station networks of the public transportation system, the base station network of the cellular communication system, and the virtual networks based on sofware defned networks (SDNs). For example, in the airport network, diferent airlines cover diferent subsets of the airports across the whole country, and airlines operate in the same airport have to share and compete for the limited resources such as space and time. In the near future, diferent communication service providers may share base stations, generating potential compe- titions for bandwidth and processing capabilities of the based stations. Te next generation of Internet may be built upon the framework of SDN, enabling one same physical server network to be virtually separated into multiple independent subnetworks with scalable sizes, each serving or being operated by a particular user without interfering with other subnetwork layers. In this case, the same server may carry the load generated by multiple layers (users), and its fnite processing capacity is competed by the layers of virtual servers. All these call for a systematic study to understand the resilience of multilayer, interdependent networks subject to internal resource competitions. Te goals of this paper are to develop a model capturing the key topological and dynamical features of the multilayer infrastructures incor- porating inter-layer resource competitions, to study the extreme event dynamics from the standpoint of 1 School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA. 2 Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou Gansu 730000, China. 3 School of Mathematical Science, Anhui University, Hefei 230039, China. 4 School of Sustainable engineering and Built Environment, Arizona State University, Tempe, AZ 85287, USA. 5 Department of Physics, Arizona State University, Tempe, Arizona 85287, USA. Correspondence and requests for materials should be addressed to Y.-C.L. (email: Ying-Cheng.Lai@asu.edu) received: 08 September 2015 Accepted: 28 October 2015 Published: 27 November 2015 opeN