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本文对簇间连接方式不同的三类簇网络的同步能力和同步过程进行研究. 构成簇网络的两个子网均为BA无标度网络, 当簇间连接方式是双向耦合时, 称其为TWD网络模型, 当簇间连接是大子网驱动小子网时, 称其为BDS网络模型, 当簇间连接是小子网驱动大子网时, 称其为SDB网络模型. 研究表明, 当小子网和大子网节点数目的比值大于某一临界值时, TWD网络模型的同步能力大于BDS网络模型的同步能力, 当该比值小于某一临界值时, TWD网络模型的同步能力小于BDS网络模型的同步能力, SDB网络模型的同步能力是三种网络结构中最差的. 对于簇间连接具有方向性的单向驱动网络, 簇网络的整体同步能力与被驱动子网的节点数和簇间连接数有关, 与驱动网络自身节点数无关. 增加簇间连接数在开始时会降低各子网的同步速度, 但最终各子网到达完全同步的时间减少, 网络的整体同步能力增强. 文中以Kuramoto相振子作为网络节点, 研究了不同情况下三种簇网络的同步过程, 证明了所得结论的正确性.
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关键词:
- 簇网络 /
- 有向连接 /
- 同步能力 /
- Kuramoto振子
This paper studies the synchronizability and the synchronization processes of three kinds of clustered networks with different inter-cluster couplings, where each clustered network is composed of two BA scale-free subnets. The clustered network is called a TWD network if the inter-cluster coupling is a two-way coupling, but it is called a BDS network if the small subnet is driven by the big one, and is called an SDB network if the big subnet is driven by the small one. The result shows that when the ratio of node number of small subnet to that of big one is larger than a critical value, the whole synchronizability of the TWD networks is better than that of the BDS networks; however, when this ratio is smaller than the critical value, the whole synchronizability of the TWD networks is weaker than that of the BDS ones, the whole synchronizability of the SDB networks is always the worst. For a one-way-driven clustered network, the synchronizability is just related to the node number of the driven subnet and the number of the inter-links, but has nothing to do with the node number of the driving subnet. The increase in the inter-links can reduce the synchronous speed of the subnet at the beginning but may enhance the synchronizability of the whole network eventually. The Kuramoto phase oscillators are taken as the network nodes to further study the synchronization process of the three-clustered networks for different cases, and the correctness of the above conclusions are evidenced.[1] Wang X F, Li X, Chen G R 2006 Theory and Applications of complex network (1st Ed.) (Beijing: Tsinghua University Press) 162-164, 194-199, 299-332
[2] Wasserman S, Faust K 1994 Social network analysis: Methord and applications (1st Ed.) (Cambridge: Cambridge University press) 35-41
[3] Scott J 2000 Social Network Analysis: A Handbook (2nd ed.)(SAGE Publications) 123-165
[4] Patrick N, McGraw, Menzinger M 2005 Phys. Rev. E 72 015101
[5] Lai D R, Nardini C, Lu H T 2011 Phys. Rev. E 83 016115
[6] Leicht E A, Clarksou G, Shedden K, Newman M E J 2007 Europhys. B 59 75
[7] Wang X F 2002 Int. J. Bifurcation Chaos 12 885
[8] Lar D R 2011 Ph. D. Dissertation (Shanghai Jiaotong Universty) (in Chinese) [赖大荣 2011 博士学位论文(上海: 上海交通大学)]
[9] Juan A, Acebrón, Bonilla L L, Conrad J, Pérez Vicente, Félix Ritort, Renato Spigler 2005 Rev. Mod. Phys. 77 137
[10] Moreno Y, Pacheco A F 2004 Europhys. Lett. 68 603
[11] Sorrentino F, Ott E 2007 Phys. Rev. E 76 056114
[12] Zou Y L, Zhu J, Chen G 2006 Phys. Rev. E 74 046107
[13] Zou Y L, Chen G 2008 Europhys. Lett. 84 58005
[14] Zou Y L, Chen G 2009 Phys. A 388 2931
[15] Zou Y L, Chen G 2009 Chin. Phys. B 18 3337
[16] Zhu T X, Wu Y, Xiao J H 2012 Acta Phys. Sin. 61 040502 (in Chinese) [朱廷祥, 吴晔, 肖井华 2012 物理学报 61 040502]
[17] Ma X J, Wang Y, Zheng Z G 2009 Acta Phys. Sin. 58 4426 (in Chinese) [马晓娟, 王延, 郑志刚 2009 物理学报 58 4426]
[18] Sun Y Z, Tang Y F 2010 Chin. Phys. B 19 020506
[19] Lu X Q, Austin F, Chen S H 2010 Chin. Phys. Lett. 27 050503
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[1] Wang X F, Li X, Chen G R 2006 Theory and Applications of complex network (1st Ed.) (Beijing: Tsinghua University Press) 162-164, 194-199, 299-332
[2] Wasserman S, Faust K 1994 Social network analysis: Methord and applications (1st Ed.) (Cambridge: Cambridge University press) 35-41
[3] Scott J 2000 Social Network Analysis: A Handbook (2nd ed.)(SAGE Publications) 123-165
[4] Patrick N, McGraw, Menzinger M 2005 Phys. Rev. E 72 015101
[5] Lai D R, Nardini C, Lu H T 2011 Phys. Rev. E 83 016115
[6] Leicht E A, Clarksou G, Shedden K, Newman M E J 2007 Europhys. B 59 75
[7] Wang X F 2002 Int. J. Bifurcation Chaos 12 885
[8] Lar D R 2011 Ph. D. Dissertation (Shanghai Jiaotong Universty) (in Chinese) [赖大荣 2011 博士学位论文(上海: 上海交通大学)]
[9] Juan A, Acebrón, Bonilla L L, Conrad J, Pérez Vicente, Félix Ritort, Renato Spigler 2005 Rev. Mod. Phys. 77 137
[10] Moreno Y, Pacheco A F 2004 Europhys. Lett. 68 603
[11] Sorrentino F, Ott E 2007 Phys. Rev. E 76 056114
[12] Zou Y L, Zhu J, Chen G 2006 Phys. Rev. E 74 046107
[13] Zou Y L, Chen G 2008 Europhys. Lett. 84 58005
[14] Zou Y L, Chen G 2009 Phys. A 388 2931
[15] Zou Y L, Chen G 2009 Chin. Phys. B 18 3337
[16] Zhu T X, Wu Y, Xiao J H 2012 Acta Phys. Sin. 61 040502 (in Chinese) [朱廷祥, 吴晔, 肖井华 2012 物理学报 61 040502]
[17] Ma X J, Wang Y, Zheng Z G 2009 Acta Phys. Sin. 58 4426 (in Chinese) [马晓娟, 王延, 郑志刚 2009 物理学报 58 4426]
[18] Sun Y Z, Tang Y F 2010 Chin. Phys. B 19 020506
[19] Lu X Q, Austin F, Chen S H 2010 Chin. Phys. Lett. 27 050503
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