有向相依网络的可控性研究
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摘要
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。
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 outdegree nodes. The research results provide a useful reference and guidance for the construction of actual interdependent directed 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 outdegree nodes. The research results provide a useful reference and guidance for the construction of actual interdependent directed networks.
引文
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[22]NIE Sen,WANG Xuwen,WANG Binghong.Effect of degree correlation on exact controllability of multiplex networks[J].Physica A:statistical mechanics and its applications,2015,436:98-102.
[2]NEWMAN M E,GIRVAN M.Finding and evaluating community structure in networks[J].Physical review E,2004,69(2):026113.
[3]SHEN J,ZHENG B.Cross-correlation in financial dynamics[J].Europhysics letters,2009,86(4):48005.
[4]LIN Chingtai.Structural controllability[J].IEEE transactions on automatic control,1974,19(3):201-208.
[5]LIU Yangyu,SLOTINE J J,BARABáSI A L.Controllability of complex networks[J].Nature,2011,473(7346):167-173.
[6]JIA Tao,LIU Yangyu,CSóKA E,et al.Emergence of bimodality in controlling complex networks[J].Nature communications,2013,4:2002.
[7]JIA Tao,BARABáSI A L.Control capacity and a random sampling method in exploring controllability of complex networks[J].Scientific reports,2013,3:2354.
[8]WANG Wenxu,NI Xuan,LAI Yingcheng,et al.Optimizing controllability of complex networks by minimum structural perturbations[J].Physical review E,2012,85(2):026115.
[9]XU Jiuqiang,WANG Jinfang,ZHAO Hai,et al.Improving controllability of complex networks by rewiring links regularly[C]//Proceedings of the 26th Chinese Control and Decision Conference.Changsha,China:IEEE,2014:642-645.
[10]HOU Lvlin,LAO Songyang,SMALL M,et al.Enhancing complex network controllability by minimum link direction reversal[J].Physics letters A,2015,379(20/21):1321-1325.
[11]YUAN Zhengzhong,ZHAO Chen,DI Zengru,et al.Exact controllability of complex networks[J].Nature communications,2013,4:2447.
[12]LI Jingwen,YUAN Zhengzhong,FAN Ying,et al.Controllability of fractal networks:an analytical approach[J].Europhysics letters,2014,105(5):58001.
[13]BULDYREV S V,PARSHANI R,PAUL G,et al.Catastrophic cascade of failures in interdependent networks[J].Nature,2010,464(7291):1025-1028.
[14]WANG Jianwei,LI Yun,ZHENG Qiaofang.Cascading load model in interdependent networks with coupled strength[J].Physica A:statistical mechanics and its applications,2015,430:242-253.
[15]WANG Jianwei,JIANG Chen,QIAN Jianfei.Robustness of interdependent networks with different link patterns against cascading failures[J].Physica A:statistical mechanics and its applications,2014,393:535-541.
[16]CHENG Zunshui,CAO Jinde.Cascade of failures in interdependent networks coupled by different type networks[J].Physica A:statistical mechanics and its applications,2015,430:193-200.
[17]陈世明,吕辉,徐青刚,等.基于度的正/负相关相依网络模型及其鲁棒性研究[J].物理学报,2015,64(4):048902.CHEN Shiming,LüHui,XU Qinggang,et al.The model of interdependent network based on positive/negative correlation of the degree and its robustness study[J].Acta physica sinica,2015,64(4):048902.
[18]GóMEZ S,DíAZ-GUILERA A,GóMEZ-GARDE?ESJ,et al.Diffusion dynamics on multiplex networks[J].Physical review letters,2013,110(2):028701.
[19]OHTSUKI H,NOWAK M A,PACHECO J M.Breaking the symmetry between interaction and replacement in evolutionary dynamics on graphs[J].Physical review letters,2007,98(10):108106.
[20]BARRETO E,HUNT B,OTT E,et al.Synchronization in networks of networks:the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators[J].Physical review E,2007,77(3):036107.
[21]YUAN Zhengzhong,ZHAO Chen,WANG Wenxu,et al.Exact controllability of multiplex networks[J].New journal of physics,2014,16(10):103036.
[22]NIE Sen,WANG Xuwen,WANG Binghong.Effect of degree correlation on exact controllability of multiplex networks[J].Physica A:statistical mechanics and its applications,2015,436:98-102.