A Method for Finding Constrained Driver Nodes in Target Control of Network

Abstract

One of the ultimate goals of studying network dynamics and its properties is to control it. In the past 20 years, with the joint efforts of many scientists, the theory of controlling a whole network through a small set of nodes, which are called driver nodes (DN) has made great progress. However, the full control of networks may be neither feasible nor necessary in some real systems with huge size and high complexity, which motivate scientists to explore target control theory, i.e., the efficient control for a subset of nodes in a network through a small node set. And in a real network, there is another common situation, which is not each node can be easily accessed. Therefore, it is meaningful to explore the target control strategy under the condition that the driver nodes are constrained. In this paper, an effective method is proposed to make more DN be included in the constrained node set (CNs). We adopt the strategy of greedy algorithm to gradually constrain DN into CNs in the iterative process of target control. In each iteration, we will adjust the strategy of how to choose driver nodes according to some network properties. And a few experiments were presented to prove that the proposed method can make DN into CNs effectively in both Scale-free networks (SF) and Erdös-Rényi (ER) networks. Then, we explored the performance of this method in the case of local and random selection of target nodes, respectively. In addition, some factors that will affect the effects of this method were also explored in this paper. In the end, this method is proved valid through the verification of the real network data sets.