title: Onset of cooperation between layered networks.
abstract: Functionalities of a variety of complex systems involve cooperations among multiple components; for example, a transportation system provides convenient transfers among airlines, railways, roads, and shipping lines. A layered model with interacting networks can facilitate the description and analysis of such systems. In this paper we propose a model of traffic dynamics and reveal a transition at the onset of cooperation between layered networks. The cooperation strength, treated as an order parameter, changes from zero to positive at the transition point. Numerical results on artificial networks as well as two real networks, Chinese and European railway-airline transportation networks, agree well with our analysis.
authors.affiliation: College of Physics Science and Technology, Yangzhou University, Yangzhou 225002, PR China.
authors.forename: Chang-Gui
authors.initials: CG
authors.lastname: Gu
authors.forename: Sheng-Rong
authors.initials: SR
authors.lastname: Zou
authors.forename: Xiu-Lian
authors.initials: XL
authors.lastname: Xu
authors.forename: Yan-Qing
authors.initials: YQ
authors.lastname: Qu
authors.forename: Yu-Mei
authors.initials: YM
authors.lastname: Jiang
authors.forename: Da Ren
authors.initials: DR
authors.lastname: He
authors.forename: Hong-Kun
authors.initials: HK
authors.lastname: Liu
authors.forename: Tao
authors.initials: T
authors.lastname: Zhou