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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 56 6851]
[11] Lü L, Xia X L 2009 Acta Phys. Sin. 58 814 (in Chinese) [吕 翎、 夏晓岚 2009 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 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 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 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 56 6851]
[11] Lü L, Xia X L 2009 Acta Phys. Sin. 58 814 (in Chinese) [吕 翎、 夏晓岚 2009 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 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 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 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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