Target control based on edge dynamics in complex networks

Furong Lu,Yuhua Qian,Kaikai Yang

doi:10.1038/s41598-020-66524-6

Abstract

In the past decade, the study of the dynamics of complex networks has been a focus of research. In particular, the controllability of complex networks based on the nodal dynamics has received strong attention. As a result, significant theories have been formulated in network control. Target control theory is one of the most important results among these theories. This theory addresses how to select as few input nodes as possible to control the chosen target nodes in a nodal linear dynamic system. However, the research on how to control the target edges in switchboard dynamics, which is a dynamical process defined on the edges, has been lacking. This shortcoming has motivated us to give an effective control scheme for the target edges. Here, we propose the k-travel algorithm to approximately calculate the minimum number of driven edges and driver nodes for a directed tree-like network. For general cases, we put forward a greedy algorithm TEC to approximately calculate the minimum number of driven edges and driver nodes. Analytic calculations show that networks with large assortativity coefficient as well as small average shortest path are efficient in random target edge control, and networks with small clustering coefficient are efficient in local target edge control.

Highlights

In the past decade, the study of the dynamics of complex networks has been a focus of research
Tamas Nepusz et al study the formation of an edge dynamics system and analyse the structural controllability of edge dynamics[13], which transforms the edge dynamics in the original networks into the nodal dynamics in the corresponding linear graph
For the problem of a single edge input, we propose a k-travel theory based on the edge dynamics

Summary

Method

The dynamical processes performed in the vast majority of systems are nonlinear. Given a directed network G(V, E) where |V| = N and E = L denote the number of vertexes and edges, if aji ≠ 0 is in the matrix A, there is a link from node i to node j. Based on the switchboard dynamics, we use this k-travel theory to give an effective algorithm to find the controllable set of any edge in the directed tree, especially the root edge. We can prove that the driven edges and driver nodes obtained by our algorithm can control the target edges The main processes of the TEC algorithm are shown, and they are based on structural control theory[5,6] as well as the edge dynamics[13].

Result

Discussion