有向相依网络的可控性研究

针对相依方式对有向相依网络可控性的影响，研究了不同相依方式下有向相依网络的可控性。通过构建基本的有向相依网络模型，结合严格可控性理论，给出了可控性评判指标。同时基于经典的有向随机网络和有向无标度网络，提出3种有向相依网络模型，并研究了随机相依条件下有向相依网络的可控性。随后定义了3种相依方式，并对比分析了在不同相依方式下有向相依网络的可控性。结果表明，在同等相依比例下，基于最低入度与最低出度节点相依的有向相依网络可控性最强，而基于最高入度与最高出度节点相依的有向相依网络可控性最弱，研究成果能够为实际有向相依网络的构建提供有益的参考和指导。

Research on the controllability of directed interdependent networks

In this paper, we consider the influence of interdependency on the controllability of interdependent directed networks and investigate the controllability of interdependent directed networks with different types of interdependency. We build a basic interdependent directed network model and generate a controllability index by introducing the theory of exact controllability. We propose three kinds of interdependent directed network models for classical directed random networks and directed scale-free networks. In addition, we investigate the controllability of the interdependent directed networks with random interdependencies. Based on the results, we propose three kinds of interdependencies and compare and analyze the controllability of interdependent directed networks with different types of interdependency. The results show that, with the same proportion of interdependence, the best controllability of an interdependent directed network is that with an interdependency of lowest in-degree and lowest out-degree nodes, whereas the poorest controllability of an interdependent directed network is that with an interdependency of highest in-degree and highest out-degree nodes. The research results provide a useful reference and guidance for the construction of actual interdependent directed networks.