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以Plankton时空混沌系统作为网络节点,通过非线性耦合构成富社团(rich-club,RC)网络,研究其时空混沌同步规律.首先给出了RC网络中连接节点之间的非线性耦合函数的一般性选取原则.进而基于Lyapunov稳定性定理,理论分析了实现网络同步的条件.最后,通过仿真模拟检验了网络的时空混沌同步效果.仿真研究表明,RC网络中各富节点之间以及这些富节点各自星形连接的子网络中的所有节点均实现了完全同步.
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关键词:
- 同步 /
- 时空混沌 /
- 富社团网络 /
- Lyapunov稳定性定理
The Plankton spatiotemporal chaos system is taken as network node and constructed as a rich-club network through nonlinear coupling. The synchronization of spatiotemporal chaos for the above network is investigated. The general selection rule of nonlinear coupling function connecting nodes in the rich-club network is presented. Furthermore, the condition to realize the network synchronization is analyzed theoretically based on Lyapunov stability theory. Finally, the synchronization effect of spatiotemporal chaos for the rich-club network is checked through artificial simulation. The results show that complete synchronization can be realized for all rich nodes in the rich-club network and all nodes in every subnetwork constructed in star-shape.[1] Watts D J, Strogatz S H 1998 Nature 393 440
[2] Albert R, Jeong H, Barabsi A L 1999 Nature 401 130
[3] Adamic L A, Huberman B A 2000 Science 287 2115
[4] Newman M E J, Strogatz S H, Watts D J 2001 Phys. Rev. E 64 26118
[5] Stelling J, Klamt S, Bettenbrock K, Schuster S, Gilles E D 2002 Nature 420 190
[6] Strogatz S H 2001 Nature 410 268
[7] Ravasz E, Barabsi A L 2003 Phys. Rev. E 67 26112
[8] Vzquez A, Pastor-Satorras R, Vespignani A 2002 Phys. Rev. E 65 66130
[9] Huang L, Kwangho P, Lai Y C, Yang L, Yang K Q 2006 Phys. Rev. Lett. 97 164101
[10] Zhang R, Hu A H, Xu Z Y 2007 Acta Phys. Sin. 56 6851 (in Chinese)[张 荣、 胡爱花、 徐振源 2007 物理学报 56 6851]
[11] Lü L, Xia X L 2009 Acta Phys. Sin. 58 814 (in Chinese) [吕 翎、 夏晓岚 2009 物理学报 58 814]
[12] Lü L, Chai Y, Luan L 2010 Chin.Phys. B 19 080506
[13] 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]
[14] Hennig D, Schimansky-Geier L 2008 Physica A 387 967
[15] Li Y, Lü L, Luan L 2009 Acta Phys. Sin. 58 4463 (in Chinese)[李 岩、 吕 翎、 栾 玲 2009 物理学报 58 4463]
[16] Gao Y, Li L X, Peng H P, Yang Y X, Zhang X H 2008 Acta Phys. Sin. 57 2081 (in Chinese) [高 洋、 李丽香、 彭海朋、 杨义先、 张小红 2008 物理学报 57 2081]
[17] Wu C W, Chua L O 1995 IEEE Trans. Circuits Syst. Ⅰ 42 430
[18] Gade P M, Hu C K 2000 Phys. Rev. E 62 6409
[19] Wang X F, Chen G R 2002 J. Bifur. Chaos 12 187
[20] Checco P, Biey M, Kocarev L 2008 Chaos Soliton. Fract. 35 562
[21] Timme M, Wolf F, Geisel T 2004 Phys. Rev. Lett. 92 74101
[22] He G M, Yang J Y 2008 Chaos Soliton. Fract. 38 1254
[23] Hung Y C, Huang Y T, Ho M C, Hu C K 2008 Phys. Rev. E 77 16202
[24] Lü J H, Yu X H, Chen G R 2004 Physica A 334 281
[25] Lü L 2000 Nonlinear Dynamics and Chaos (Dalian: Dalian Publishing House) (in Chinese) [吕 翎 2000 非线性动力学与混沌 (大连: 大连出版社)]
[26] Malchow H, Radtke B, Kallache M, Medvinsky A B, Tikhonov D A, Petrovskii S V 2000 Nonlinear Anal.: Real. World Appl. 1 53
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[1] Watts D J, Strogatz S H 1998 Nature 393 440
[2] Albert R, Jeong H, Barabsi A L 1999 Nature 401 130
[3] Adamic L A, Huberman B A 2000 Science 287 2115
[4] Newman M E J, Strogatz S H, Watts D J 2001 Phys. Rev. E 64 26118
[5] Stelling J, Klamt S, Bettenbrock K, Schuster S, Gilles E D 2002 Nature 420 190
[6] Strogatz S H 2001 Nature 410 268
[7] Ravasz E, Barabsi A L 2003 Phys. Rev. E 67 26112
[8] Vzquez A, Pastor-Satorras R, Vespignani A 2002 Phys. Rev. E 65 66130
[9] Huang L, Kwangho P, Lai Y C, Yang L, Yang K Q 2006 Phys. Rev. Lett. 97 164101
[10] Zhang R, Hu A H, Xu Z Y 2007 Acta Phys. Sin. 56 6851 (in Chinese)[张 荣、 胡爱花、 徐振源 2007 物理学报 56 6851]
[11] Lü L, Xia X L 2009 Acta Phys. Sin. 58 814 (in Chinese) [吕 翎、 夏晓岚 2009 物理学报 58 814]
[12] Lü L, Chai Y, Luan L 2010 Chin.Phys. B 19 080506
[13] 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]
[14] Hennig D, Schimansky-Geier L 2008 Physica A 387 967
[15] Li Y, Lü L, Luan L 2009 Acta Phys. Sin. 58 4463 (in Chinese)[李 岩、 吕 翎、 栾 玲 2009 物理学报 58 4463]
[16] Gao Y, Li L X, Peng H P, Yang Y X, Zhang X H 2008 Acta Phys. Sin. 57 2081 (in Chinese) [高 洋、 李丽香、 彭海朋、 杨义先、 张小红 2008 物理学报 57 2081]
[17] Wu C W, Chua L O 1995 IEEE Trans. Circuits Syst. Ⅰ 42 430
[18] Gade P M, Hu C K 2000 Phys. Rev. E 62 6409
[19] Wang X F, Chen G R 2002 J. Bifur. Chaos 12 187
[20] Checco P, Biey M, Kocarev L 2008 Chaos Soliton. Fract. 35 562
[21] Timme M, Wolf F, Geisel T 2004 Phys. Rev. Lett. 92 74101
[22] He G M, Yang J Y 2008 Chaos Soliton. Fract. 38 1254
[23] Hung Y C, Huang Y T, Ho M C, Hu C K 2008 Phys. Rev. E 77 16202
[24] Lü J H, Yu X H, Chen G R 2004 Physica A 334 281
[25] Lü L 2000 Nonlinear Dynamics and Chaos (Dalian: Dalian Publishing House) (in Chinese) [吕 翎 2000 非线性动力学与混沌 (大连: 大连出版社)]
[26] Malchow H, Radtke B, Kallache M, Medvinsky A B, Tikhonov D A, Petrovskii S V 2000 Nonlinear Anal.: Real. World Appl. 1 53
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