2.624

2020影响因子

(CJCR)

  • 中文核心
  • EI
  • 中国科技核心
  • Scopus
  • CSCD
  • 英国科学文摘

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

复杂网络同步态与孤立节点解的关系

陈娟 陆君安 周进

陈娟, 陆君安, 周进. 复杂网络同步态与孤立节点解的关系. 自动化学报, 2013, 39(12): 2111-2120. doi: 10.3724/SP.J.1004.2013.02111
引用本文: 陈娟, 陆君安, 周进. 复杂网络同步态与孤立节点解的关系. 自动化学报, 2013, 39(12): 2111-2120. doi: 10.3724/SP.J.1004.2013.02111
CHEN Juan, LU Jun-An, ZHOU Jin. On the Relationship between the Synchronous State and the Solution of an Isolated Node in a Complex Network. ACTA AUTOMATICA SINICA, 2013, 39(12): 2111-2120. doi: 10.3724/SP.J.1004.2013.02111
Citation: CHEN Juan, LU Jun-An, ZHOU Jin. On the Relationship between the Synchronous State and the Solution of an Isolated Node in a Complex Network. ACTA AUTOMATICA SINICA, 2013, 39(12): 2111-2120. doi: 10.3724/SP.J.1004.2013.02111

复杂网络同步态与孤立节点解的关系

doi: 10.3724/SP.J.1004.2013.02111
基金项目: 

国家自然科学基金(11172215,61004096,61174028,61304164,61374173)资助

详细信息
    作者简介:

    陈娟 博士,武汉科技大学理学院讲师. 主要研究方向为复杂网络,非线性系统,混沌控制与同步.E-mail:jc1204@126.com

On the Relationship between the Synchronous State and the Solution of an Isolated Node in a Complex Network

Funds: 

Supported by National Natural Science Foundation of China (11172215, 61004096, 61174028, 61304164, 61374173)

  • 摘要: 复杂网络同步是复杂系统和复杂网络的前沿研究方向之一,已经取得很大的进展. 但是对于节点以耦合矩阵左特征向量加权平均态、孤立节点的解与网络的同步态之间具有什么关系,什么是网络的同步态和同步轨等基本问题仍然缺乏深入的研究,弄清楚这些问题对于复杂网络同步的理解和应用具有重要的意义. 本文采用数学分析方法证明,如果网络同步,则加权平均态 x = j=1Njxj可以定义为同步态,一般来说,x在正极限集的意义下,也就是孤立节点方程的解. 因此在实际应用中,把孤立节点方程的解s(t) 与加权平均态x不加区别地对待是合理的. 同步态是不依赖于初始条件的通解,而同步轨是依赖于初始条件的特解. 对于混沌节点的网络,同步态应该理解为吸引子,而不是某一条轨道. 最后,本文还提供一些实例加以说明,并指出一些尚待解决的问题.
  • [1] Watts D J, Strogatz S H. Collective dynamics of small-world network. Nature, 1998, 393(6684): 440-442
    [2] [2] Barabsi A L, Albert R. Emergence of SCAling in random networks. Science, 1999, 286(5439): 509-512
    [3] [3] Newman M E J. Models of the small world: a review. Journal of Statistical Physics, 2000, 101(3-4): 819-841
    [4] [4] Strogatz S H. Exploring complex networks. Nature, 2001, 410(6825): 268-276
    [5] [5] Albert R, Barabsi A L. Statistical mechanics of complex networks. Reviews of Modern Physics, 2002, 74(1): 47-97
    [6] [6] Newman M E J. The structure and function of complex networks. SIAM Review, 2003, 45(2): 167-256
    [7] Chen Guan-Rong. Problems and challenges in control theory under complex dynamical network environments. Acta Automatica Sinica, 2013, 39(4): 312-321 (陈关荣. 复杂动态网络环境下控制理论遇到的问题与挑战. 自动化学报, 2013, 39(4): 312-321)
    [8] [8] Pecora L M, Carroll T L. Synchronization in chaotic systems. Physical Review Letters, 1990, 64(8): 821-824
    [9] [9] Wu C W, Chua L O. Synchronization in an array of linearly coupled dynamical systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1995, 42(8): 430-447
    [10] Pecora L M, Carroll T L. Master stability functions for synchronized coupled systems. Physical Review Letters, 1998, 80(10): 2109-2112
    [11] Pecora L, Carroll T, Johnson G, Mar D, Fink K S. Synchronization stability in coupled oscillator arrays: solution for arbitrary configurations. International Journal of Bifurcation and Chaos, 2000, 10(2): 273-290
    [12] Wang X F, Chen G R. Synchronization in SCAle-free dynamical networks: robustness and fragility. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2002, 49(1): 54-62
    [13] Wang X F, Chen G R. Synchronization in small-world dynamical networks. International Journal of Bifurcation and Chaos, 2002, 12(1): 187-192
    [14] Motter A E, Zhou C S, Kurths J. Network synchronization, diffusion, and the paradox of heterogeneity. Physical Review E, 2005, 71(1): 016116
    [15] Nishikawa T, Motter A E. Maximum performance at minimum cost in network synchronization. Physica D: Nonlinear Phenomena, 2006, 224(1-2): 77-89
    [16] Wang Xiao-Fan, Li Xiang, Chen Guan-Rong. Theory and Application of Complex Networks. Beijing: Tsinghua University Press, 2006. 194-240 (汪小帆, 李翔, 陈关荣. 复杂网络理论及其应用. 北京: 清华大学出版社, 2006. 194-240)
    [17] Arenas A, Daz-Guilera A, Kurths J, Moreno Y, Zhou C S. Synchronization in complex networks. Physics Reports, 2008, 469(3): 93-153
    [18] Wu C W. Synchronization in Complex Networks of Nonlinear Dynamical Systems. Singapore: World Scientific Publishing Company, 2007
    [19] Olfati-Saber R, Murray R M. Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control, 2004, 49(9): 1520-1533
    [20] Wu C W. Synchronization in networks of nonlinear dynamical systems coupled via a directed graph. Nonlinearity, 2005, 18(3): 1057-1064
    [21] Lu W L, Chen T P. New approach to synchronization analysis of linearly coupled ordinary differential systems. Physica D: Nonlinear Phenomena, 2006, 213(2): 214-230
    [22] Zhou J, Lu J A, Lv J H. Adaptive synchronization of an uncertain complex dynamical network. IEEE Transactions on Automatic Control, 2006, 51(4): 652-656
    [23] Yu W W, DeLellis P, Chen G R, di Bernardo M, Kurths J. Distributed adaptive control of synchronization in complex networks. IEEE Transactions on Automatic Control, 2012, 57(8): 2153-2158
    [24] Yang X S, Cao J D, Lu J Q. Stochastic synchronization of complex networks with nonidentical nodes via hybrid adaptive and impulsive control. IEEE Transactions on Circuits and Systems I: Regular Papers, 2012, 59(2): 371-384
    [25] Liu B, Lu W L, Chen T P. Synchronization in complex networks with stochastically switching coupling structures. IEEE Transactions on Automatic Control, 2012, 57(3): 754 -760
    [26] Drfler F, Bullo F. Synchronization and transient stability in power networks and nonuniform Kuramoto oscillators. SIAM Journal on Control and Optimization, 2012, 50(3): 1616-1642
    [27] Winfree A T. The Geometry of Biological Time. New York: Springer Verlag, 2001
    [28] Khalil H K. Nonlinear Systems. London: Prentice Hall, 2002. 191-196
  • 加载中
计量
  • 文章访问数:  1802
  • HTML全文浏览量:  41
  • PDF下载量:  1385
  • 被引次数: 0
出版历程
  • 收稿日期:  2013-02-26
  • 修回日期:  2013-08-01
  • 刊出日期:  2013-12-20

目录

    /

    返回文章
    返回