title: Growth, collapse, and self-organized criticality in complex networks.
abstract: Network growth is ubiquitous in nature (e.g., biological networks) and technological systems (e.g., modern infrastructures). To understand how certain dynamical behaviors can or cannot persist as the underlying network grows is a problem of increasing importance in complex dynamical systems as well as sustainability science and engineering. We address the question of whether a complex network of nonlinear oscillators can maintain its synchronization stability as it expands. We find that a large scale avalanche over the entire network can be triggered in the sense that the individual nodal dynamics diverges from the synchronous state in a cascading manner within a relatively short time period. In particular, after an initial stage of linear growth, the network typically evolves into a critical state where the addition of a single new node can cause a group of nodes to lose synchronization, leading to synchronization collapse for the entire network. A statistical analysis reveals that the collapse size is approximately algebraically distributed, indicating the emergence of self-organized criticality. We demonstrate the generality of the phenomenon of synchronization collapse using a variety of complex network models, and uncover the underlying dynamical mechanism through an eigenvector analysis.
authors.affiliation: School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China.
authors.forename: Yafeng
authors.initials: Y
authors.lastname: Wang
authors.affiliation: School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China.
authors.forename: Huawei
authors.initials: H
authors.lastname: Fan
authors.affiliation: School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China.|Department of Physics, Zhejiang University, Hangzhou 310027, China.
authors.forename: Weijie
authors.initials: W
authors.lastname: Lin
authors.affiliation: School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA.
authors.forename: Ying-Cheng
authors.initials: YC
authors.lastname: Lai
authors.affiliation: School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China.
authors.forename: Xingang
authors.initials: X
authors.lastname: Wang