Pinning control of complex dynamical networks with general topology

被引:125
作者
Xiang, L. Y. [1 ]
Liu, Z. X. [1 ]
Chen, Z. Q. [1 ]
Chen, F. [1 ]
Yuan, Z. Z. [1 ]
机构
[1] Nankai Univ, Dept Automat, Tianjin 300071, Peoples R China
基金
中国国家自然科学基金; 高等学校博士学科点专项科研基金;
关键词
complex dynamical network; directed graph; master stability function; pinning control; transverse Lyapunov exponents (TLEs); weighted networks;
D O I
10.1016/j.physa.2006.12.037
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Recently, the researches on pinning control of complex dynamical networks have mainly focused on such networks with very specific coupling schemes (e.g., symmetric coupling, uniform coupling and linear coupling). However, most real networks often consist of local units, which interact with each other via asymmetric and heterogeneous connections. In this paper, pinning control of a continuous-time complex dynamical network with general coupling topologies is studied. Some generic stability criteria based on master stability function (MSF) are derived for such a general controlled network, which guarantee that the whole network can be pinned to its equilibrium by placing feedback control only on a small fraction of nodes. Then, these results are extended to discrete-time case. Previous results about symmetric, uniform or linear coupled networks in this area are included as special cases of the present work. Numerical simulations of directed networks with weighted coupling pinned by specifically selective pinning scheme are given for illustration and verification. (c) 2007 Elsevier B.V. All rights reserved.
引用
收藏
页码:298 / 306
页数:9
相关论文
共 36 条
[1]   Statistical mechanics of complex networks [J].
Albert, R ;
Barabási, AL .
REVIEWS OF MODERN PHYSICS, 2002, 74 (01) :47-97
[2]   Emergence of scaling in random networks [J].
Barabási, AL ;
Albert, R .
SCIENCE, 1999, 286 (5439) :509-512
[3]   Synchronization in small-world systems [J].
Barahona, M ;
Pecora, LM .
PHYSICAL REVIEW LETTERS, 2002, 89 (05) :054101/1-054101/4
[4]   Graph structure in the Web [J].
Broder, A ;
Kumar, R ;
Maghoul, F ;
Raghavan, P ;
Rajagopalan, S ;
Stata, R ;
Tomkins, A ;
Wiener, J .
COMPUTER NETWORKS-THE INTERNATIONAL JOURNAL OF COMPUTER AND TELECOMMUNICATIONS NETWORKING, 2000, 33 (1-6) :309-320
[5]   Synchronizing weighted complex networks [J].
Chavez, M ;
Hwang, DU ;
Amann, A ;
Boccaletti, S .
CHAOS, 2006, 16 (01)
[6]  
Chen G, 2005, ETS 2005:10TH IEEE EUROPEAN TEST SYMPOSIUM, PROCEEDINGS, P22
[7]   Yet another chaotic attractor [J].
Chen, GR ;
Ueta, T .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1999, 9 (07) :1465-1466
[8]  
Cvetkovic D., 1995, Spectra of Graphs-Theory and Application, V3rd ed.
[9]   Synchronization in stochastic coupled systems: theoretical results [J].
Deng, YC ;
Ding, MZ ;
Feng, JF .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2004, 37 (06) :2163-2173
[10]   ERGODIC-THEORY OF CHAOS AND STRANGE ATTRACTORS [J].
ECKMANN, JP ;
RUELLE, D .
REVIEWS OF MODERN PHYSICS, 1985, 57 (03) :617-656