Exact controllability of multiplex networks

Abstract

We develop a general framework to analyze the controllability of multiplex networks using multiple-relation networks and multiple-layer networks with interlayer couplings as two classes of prototypical systems. In the former, networks associated with different physical variables share the same set of nodes and in the latter, diffusion processes take place. We find that, for a multiplerelation network, a layer exists that dominantly determines the controllability of the whole network and, for a multiple-layer network, a small fraction of the interconnections can enhance the controllability remarkably. Our theory is generally applicable to other types of multiplex networks as well, leading to significant insights into the control of complex network systems with diverse structures and interacting patterns.

Control principles of complex systems

“…Early attempts have focused on the issues of controllability or observability with linear dynamics (Chapman et al, 2014;Menichetti et al, 2015;Wang et al, 2015;Yuan et al, 2014;Zhang et al, 2016;Zhou, 2015). For example, some controllability conditions on the overall network topology, the node dynamics, the external control inputs and the inner interactions have been derived for a networked MIMO system .…”

Effect of degree correlation on exact controllability of multiplex networks

“…[20] focused on the exact controllability of multiplex networks and pointed out that the controllability of multiplex networks can be affected by the density of interconnections between layers. The multiplex networks have also been studied widely in cascading failures [21,22], evolutionary game dynamics [23,24], traffic dynamics [25] and other fields of dynamical complex networks [26][27][28].…”

Exact controllability of linear dynamical systems: A~geometrical approach

“…In this paper, we analyze the exact controllability concept that, following [11], [10], is based on the maximum multiplicity, to identify the minimum set of driver nodes required to achieve full control of networks with arbitrary structures and linkweight distributions; we focus the study on the obtention of the set of all matrices B making the systemẋ(t) = Ax(t) + Bu(t) exactly controllable. We have included several examples in order to make the work easier readable and it is completed with an example in the case of an undirected network.…”