|
|
|
Outer synchronization between two different fractional-order general complex dynamical networks |
| Wu Xiang-Jun (武相军), Lu Hong-Tao (卢宏涛) |
| Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China |
|
|
|
|
Abstract Outer synchronization between two different fractional-order general complex dynamical networks is investigated in this paper. Based on the stability theory of the fractional-order system, the sufficient criteria for outer synchronization are derived analytically by applying the nonlinear control and the bidirectional coupling methods. The proposed synchronization method is applicable to almost all kinds of coupled fractional-order general complex dynamical networks. Neither a symmetric nor irreducible coupling configuration matrix is required. In addition, no constraint is imposed on the inner-coupling matrix. Numerical examples are also provided to demonstrate the validity of the presented synchronization scheme. Numeric evidence shows that both the feedback strength k and the fractional order α can be chosen appropriately to adjust the synchronization effect effectively.
|
|
Accepted manuscript online:
|
|
PACS:
|
89.75.Hc
|
(Networks and genealogical trees)
|
| |
05.45.Xt
|
(Synchronization; coupled oscillators)
|
| |
02.30.Yy
|
(Control theory)
|
| |
89.20.Hh
|
(World Wide Web, Internet)
|
|
| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 60873133) and the National High Technology Research and Development Program of China (Grant No. 2007AA01Z478). |
Cite this article:
Wu Xiang-Jun (武相军), Lu Hong-Tao (卢宏涛) Outer synchronization between two different fractional-order general complex dynamical networks 2010 Chin. Phys. B 19 070511
|
| [1] |
Watts D J and Strogatz S H 1998 Nature (London) bf393 440
|
| [2] |
Barabási A L and Albert R 1999 Science bf286 509
|
| [3] |
Strogatz S H 2001 Nature (London) bf410 268
|
| [4] |
Pastor-Satorras R and Vespignani A 2001 Phys. Rev. Lett. bf86 3200
|
| [5] |
Barab'asi A L, Jeong H, Néda Z, Ravasz E, Schubert A and Vicsek T 2002 Phys. A bf311 590
|
| [6] |
Newman M E J 2003 SIAM Review bf45 167
|
| [7] |
Pecora L M, Carrol T L and Johnson G A 1998 Chaos bf7 520
|
| [8] |
Chen G and Dong X 1998 From Chaos to Order: Methodologies, Perspectives, and Applications (Singapore: World Scientific)
|
| [9] |
Qiu F, Cui B T and Ji Y 2009 Chin. Phys. B bf18 5203
|
| [10] |
Li Z K, Duan Z S and Chen G R 2009 Chin. Phys. B bf18 5228
|
| [11] |
Boccaletti S, Latora V, Morento Y, Chavez M and Hwang D U 2006 Phys. Rep. bf424 175
|
| [12] |
Zhou J, Xiang L and Liu Z 2007 Phys. A bf385 729
|
| [13] |
Arenas A, Diaz-Guilera A, Kurths J, Moreno Y and Zhou C 2008 Phys. Rep. bf469 93
|
| [14] |
Yu W, Chen G and Lü J 2009 Automatica bf45 429
|
| [15] |
Guo W, Austin F, Chen S and Sun W 2009 Phys. Lett. A bf373 1565
|
| [16] |
Chen M, Shang Y, Zhou C, Wu Y and Kurths J 2009 Chaos bf19 013105
|
| [17] |
Montbri'o E, Kurths J and Blasius B 2004 Phys. Rev. E bf70 056125
|
| [18] |
Li C P, Sun W G and Kurths J 2007 Phys. Rev. E bf76 046204
|
| [19] |
Begon M, Townsend C and Harper J 1996 Ecology: Individuals, Populations and Communities (London: Blackwell Science)
|
| [20] |
Hu M, Xu Z and Yang Y 2008 Phys. A bf387 3759
|
| [21] |
Tang H, Chen L, Lu J and Tse C K 2008 Phys. A bf387 5623
|
| [22] |
Lu X B and Qin B Z 2009 Phys. Lett. A bf373 3650
|
| [23] |
Zheng S, Dong G and Bi Q 2009 Phys. Lett. A bf373 4255
|
| [24] |
Huang H and Feng G 2009 Neural Networks bf22 869
|
| [25] |
Sun M, Zeng C, Tao Y and Tian L 2009 Phys. Lett. A bf373 3041
|
| [26] |
Li C P, Xu X, Sun W G, Xu J and Kurths J 2009 Chaos bf19 013106
|
| [27] |
Wu X, Zheng W and Zhou J 2009 Chaos bf19 013109
|
| [28] |
Tang Y, Wang Z and Fang J 2009 Chaos bf19 013112
|
| [29] |
Podlubny I 1999 Fractional Differential Equations (New York: Academic Press)
|
| [30] |
Hifer R 2001 Applications of Fractional Calculus in Physics (New Jersey: World Scientific)
|
| [31] |
Koeller R C 1984 J. Appl. Mech. bf51 299
|
| [32] |
Sun H H, Abdelwahad A A and Onaral B 1984 IEEE Trans. Automat. Contr. bf29 441
|
| [33] |
Laskin N 2000 Phys. A bf287 482
|
| [34] |
Kunsezov D, Bulagc A and Dang G D 1999 Phys. Rev. Lett. bf82 1136
|
| [35] |
Li C G and Chen G 2004 Phys. A bf341 55
|
| [36] |
Li C and Chen G 2004 Chaos, Solitons and Fractals bf22 549
|
| [37] |
Arena P, Fortuna L and Porto D 2000 Phys. Rev. E bf61 776
|
| [38] |
Caputo M 1967 Geophys. J. R. Astron. Soc. bf13 529
|
| [38] |
Xia Y W, Pananakakis G and Kamarinos Y G 1990 J. Comput. Phys. bf91 478
|
| [39] |
Diethelm K 1997 Trans. Numer. Anal. bf5 1
|
| [40] |
Diethelm K, Ford N J and Freed A D 2002 Nonlinear Dyn. bf29 3
|
| [41] |
Diethelm K and Ford N J 2002 J. Math. Anal. Appl. bf265 229
|
| [42] |
Diethelm K, Ford N J and Freed A D 2004 Numer. Algorithms bf36 31
|
| [43] |
Matignon D 1996 IMACS SMC Proceedings pp963--968, Lille, France
|
| [44] |
Ma J H and Chen Y S 2001 Appl. Math. Mech. bf22 1240
|
| [45] |
Chen W C 2008 Chaos, Solitons and Fractals bf36 1305
|
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
