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复杂网络同步态与孤立节点解的关系

DOI: 10.3724/SP.J.1004.2013.02111, PP. 2111-2120

Keywords: 复杂网络,同步态,同步轨,孤立节点

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Abstract:

?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=1Nξjxj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.

References

[1]  Watts D J, Strogatz S H. Collective dynamics of "small-world" network. Nature, 1998, 393(6684): 440-442
[2]  Newman M E J. Models of the small world: a review. Journal of Statistical Physics, 2000, 101(3-4): 819-841
[3]  Albert R, Barabási A L. Statistical mechanics of complex networks. Reviews of Modern Physics, 2002, 74(1): 47-97
[4]  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)
[5]  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
[6]  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
[7]  Wang X F, Chen G R. Synchronization in small-world dynamical networks. International Journal of Bifurcation and Chaos, 2002, 12(1): 187-192
[8]  Nishikawa T, Motter A E. Maximum performance at minimum cost in network synchronization. Physica D: Nonlinear Phenomena, 2006, 224(1-2): 77-89
[9]  Arenas A, Díaz-Guilera A, Kurths J, Moreno Y, Zhou C S. Synchronization in complex networks. Physics Reports, 2008, 469(3): 93-153
[10]  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
[11]  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
[12]  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
[13]  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
[14]  Winfree A T. The Geometry of Biological Time. New York: Springer Verlag, 2001
[15]  Barabási A L, Albert R. Emergence of SCAling in random networks. Science, 1999, 286(5439): 509-512
[16]  Strogatz S H. Exploring complex networks. Nature, 2001, 410(6825): 268-276
[17]  Newman M E J. The structure and function of complex networks. SIAM Review, 2003, 45(2): 167-256
[18]  Pecora L M, Carroll T L. Synchronization in chaotic systems. Physical Review Letters, 1990, 64(8): 821-824
[19]  Pecora L M, Carroll T L. Master stability functions for synchronized coupled systems. Physical Review Letters, 1998, 80(10): 2109-2112
[20]  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
[21]  Motter A E, Zhou C S, Kurths J. Network synchronization, diffusion, and the paradox of heterogeneity. Physical Review E, 2005, 71(1): 016116
[22]  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)
[23]  Wu C W. Synchronization in Complex Networks of Nonlinear Dynamical Systems. Singapore: World Scientific Publishing Company, 2007
[24]  Wu C W. Synchronization in networks of nonlinear dynamical systems coupled via a directed graph. Nonlinearity, 2005, 18(3): 1057-1064
[25]  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
[26]  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
[27]  D?rfler 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
[28]  Khalil H K. Nonlinear Systems. London: Prentice Hall, 2002. 191-196

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