度相关性对无向网络可控性的影响

发布时间：2018-06-10 08:58

本文选题：复杂网络 + 无向网络　；参考：《物理学报》2017年02期

【摘要】：复杂网络的可控性不仅与网络的度分布有关,还受到度相关性的影响,但这种影响在无向网络的情况下尚不清楚.本文采用模拟退火算法,通过边的重连改变网络的度相关性从而研究其对网络可控性的影响.数值模拟结果显示,在度分布不变的情况下,无向网络的可控性指标(驱动节点密度)一般随着度相关系数的增大而单调减小;进一步研究表明,双向网络和某些有向网络也遵循这种规律.无向网络的度相关系数增大意味着对应有向网络的各种度相关系数同步增大,但这些综合变化对网络可控性的影响不能简单归结为对应有向网络中各影响的叠加.本文对这种现象给出了部分解释.此外,对于无自环的大型稀疏网络,无论其同配还是异配,验证了其结构可控性与严格可控性是几乎相同的.这些研究将深化对网络可控性与网络结构之间关系的理解.
[Abstract]:The controllability of complex networks is not only related to the degree distribution of the network, but also affected by the degree dependence, but the influence is not clear in the case of undirected networks. In this paper, simulated annealing algorithm is used to study the influence of the reconnection of edges on the controllability of the network by changing the degree dependence of the network. The numerical simulation results show that the controllability index (driving node density) of the undirected network decreases monotonously with the increase of the degree correlation coefficient when the degree distribution is invariant. Bidirectional networks and some directed networks also follow this rule. The increase of the degree correlation coefficient of the undirected network means that the various degree correlation coefficients of the corresponding directed network increase synchronously, but the influence of these comprehensive changes on the controllability of the network cannot be reduced to the superposition of each effect in the corresponding directed network. This paper gives a partial explanation of this phenomenon. In addition, the structure controllability and strict controllability are almost the same for large sparse networks without self-loop, whether they are identical or heterodyne. These studies will deepen the understanding of the relationship between network controllability and network structure.
【作者单位】：云南大学物理与天文学院非线性复杂系统中心;凯里学院数学科学学院;贵州财经大学数学与统计学院;
【基金】：国家自然科学基金(批准号:11365023) 贵州省科技厅/黔东南州科技局/凯里学院科技联合基金(批准号:黔科合LH字[2014]7231) 贵州省教育厅优秀科技创新人才支持计划(批准号:黔教合KY字[2015]505)资助的课题~~
【分类号】：O157.5

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