Controlling edge dynamics in multilayer networks

• Published in: Physica A 2019-08, Vol.528, p.121273, Article 121273
• Main Authors: Pang, Shao-Peng, Li, Chao, Fang, Cong, Han, Guo-Zheng
• Format: Article
• Language: English
• Subjects: Controllability; Edge dynamics; Multilayer networks
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2019.121273

Dynamical processes occurring on the edges of complex networks universally exists in many natural and engineered systems with multiple subsystems and layers. An edge dynamical system is controllable if, with appropriate external inputs, it can be driven from any initial state to any desired state in finite time. Here, we introduce the edge dynamics in multilayer networks, and analyze its controllability. The simulation results and analytic calculation show that the lower and upper bounds of the minimum number of driver nodes and driven edges for the edge dynamics are existed in multilayer networks, and the bound values significantly differ from that of single-layer networks with the same size. The edge dynamics in a multilayer network is more strongly structurally controllable than that in a single-layer network of the same size. Moreover, simulation results indicate that the degree correlation between layers plays an important role in the edge controllability of multilayer networks. These findings force us to go beyond single-layer network structure to offer a better understanding of the controllability of edge dynamics. •A framework is proposed to analyze the edge controllability in multilayer networks.•The controllability bound of the edge dynamics is existed in multilayer networks.•The edge dynamics in multilayer networks is more strongly structurally controllable.•Degree correlation between layers play an important role in the edge controllability.