Gu, Chang-GuiCollege of Physics Science and Technology, Yangzhou University, Yangzhou, China
Zou, Sheng-RongCollege of Physics Science and Technology, Yangzhou University, Yangzhou, China
Xu, Xiu-LianCollege of Physics Science and Technology, Yangzhou University, Yangzhou, China
Qu, Yan-QingCollege of Physics Science and Technology, Yangzhou University, Yangzhou, China
Jiang, Yu-MeiCollege of Physics Science and Technology, Yangzhou University, Yangzhou, China
He, Da RenCollege of Physics Science and Technology, Yangzhou University, Yangzhou, China
Liu, Hong-KunSchool of Statistics, South Western University of Finance and Economics, Chengdu, China
Zhou, TaoWeb Sciences Center, University of Electronic Science and Technology of China, Chengdu, China - Department of Physics, University of Fribourg, Switzerland
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. - 2011, vol. 84, no. 2, p. 026101
English
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.