| 空间网络上的随机游走 |
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| 引用本文： | 钭斐玲,胡延庆,黎勇,樊瑛,狄增如.空间网络上的随机游走[J].物理学报,2012,61(17):178901-178901. |
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| 作者姓名： | 钭斐玲 胡延庆 黎勇 樊瑛 狄增如 |
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| 作者单位： | 北京师范大学管理学院系统科学系,北京师范大学复杂性研究中心,北京100875 |
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| 基金项目： | 中央高校基本科研业务费专项资金、国家自然科学基金(批准号: 60974084, 61174150)和NCET-09-0228资助的课题. |
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| 摘 要： | 本文以一维均匀环为基础, 通过添加有限数量的长程连接构造出了一维有限能量约束下的空间网络, 环上任意节点i与j之间存在一条长程连接的概率满足pijα dij-α (α≥ 0),其中dij为节点i与j之间的网格距离, 并且所有长程连接长度总和受到总能量∧=cN(c≥ 0)的约束, N为网络节点总数.通过研究该空间网络上的随机游走过程,存在最优幂指数α0 使得陷阱问题的平均首达时间最短.进一步研究发现,平均首达时间与网络规模N之间存在着幂律关系, 随着网络规模N和总能量∧的增加,最优幂指数α0单调增加,并趋近最优值1.5.
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| 关 键 词： | 空间网络 随机游走 能量约束 平均首达时间 |
| 收稿时间： | 2011-11-21 |
Random walks on spatial networks |
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| Dou Fei-Ling,Hu Yan-Qing,Li Yong,Fan Ying,Di Zeng-Ru.Random walks on spatial networks[J].Acta Physica Sinica,2012,61(17):178901-178901. |
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| Authors: | Dou Fei-Ling Hu Yan-Qing Li Yong Fan Ying Di Zeng-Ru |
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| Institution: | Department of Systems Science, School of Management and Center for Complexity Research, Beijing Normal University, Beijing 100875, China |
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| Abstract: | In this paper, we construct a cost constrained spatial network by adding long-range connections to the one-dimensional circle. The probability for a long-range connection between nodes i and j is pijα dij-α (α≥ 0), where dij is the lattice distance and the total length of the long-range connections is set to be ∧=cN(c≥ 0), where c is a positive constant and N is the network size. According to the simulation and numeric results, we find an optimal power-law exponent α0 such that the mean first-passage time is shortest. Furthermore, the shortest mean first-passage time has the power law relationships with the network size N. With the increase of network size N and the total cost ∧, the optimal power-law exponent α0 increases monotonically and approaches 1.5. |
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| Keywords: | spatial networks random walks total energy constraint mean first-passage time |
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