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利用Backstepping设计进行了复杂网络时空混沌的同步研究. 首先将实现两个混沌系统同步的Backstepping设计推广到由m个时空混沌系统构成任意结构的复杂网络的同步研究中.进一步依据稳定性理论确定了网络同步时配置系数和控制增益满足的关系. 整个网络实现同步仅需要在网络中的一个节点施加控制输入即可.进一步通过仿真实验验证了同步机理的有效性.
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关键词:
- 同步 /
- 复杂网络 /
- Backstepping设计 /
- 时空混沌
Spatiotemporal chaos synchronization of complex networks by Backstepping design is investigated. Backstepping design is extended from synchronization between two chaotic systems to the synchronization of complex network constituted spatiotemporal chaotic systems. The relation between the configuration coefficient and the control gain is identified according to the stability theory. When the control input is added to any node of the network, the network synchronization is realized. Furthermore, simulation is made to verify the effectiveness of the synchronization mechanism.-
Keywords:
- synchronization /
- complex network /
- Backstepping design /
- spatiotemporal chaos
[1] Winfree A T 1967 J. Theo. Biol. 16 15
[2] Watts D J 1998 Nature 393 440
[3] Barabási A L, Albert R 1999 Science 286 509
[4] Pecora L M, Carroll T L 1998 Phys. Rev. Lett. 80 2109
[5] Bergner A, Frasca M, Sciuto G, Buscarino A, Ngamga E J,Fortuna L, Kurths J 2012 Phys. Rev. E 85 026208
[6] Kouvaris N, Provata A, Kugiumtzis D 2010 Phys. Lett. A 374 507
[7] Song Q, Cao J D, Liu F 2010 Phys. Lett. A 374 544
[8] Li D, Leyva I, Almendral J A, Sendiña-Nadal I, Buldú J M, Havlin S, Boccaletti S 2008 Phys. Rev. Lett. 101 168701
[9] Donetti L, Hurtado P I, Muñoz M A 2005 Phys. Rev. Lett. 95 188701
[10] Yu W W, Chen G R, L J H 2009 Automatica 45 429
[11] La Rocca C E, Braunstein L A, Macri P A 2009 Phys. Rev. E 80 26111
[12] Selivanov A A, Lehnert J, Dahms T, Hövel P, Fradkov A L, Schöll E 2012 Phys. Rev. E 85 016201
[13] Sun W, Hu T S, Chen Z, Chen S H, Xiao L 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 4501
[14] Jalan S, Amritkar R E 2003 Phys. Rev. Lett. 90 014101
[15] Acebrón J A, Bonilla L L, Vicente C J P, Ritort F, Spigler R 2005 Rev. Mod. Phys. 77 137
[16] Moreno Y, Pacheco A F 2004 Europhys. Lett. 68 603
[17] Cui B T, Lou X Y 2009 Chaos, Solitons and Fractals 39 288
[18] Shang Y, Chen M Y, Kurths J 2009 Phys. Rev. E 80 027201
[19] L L, Li G, Guo L, Meng L, Zou J R, Yang M 2010 Chin. Phys. B 19 080507
[20] Zhu Q Y, Ma Y W 2000 Comput. Mech. 17 379 (in Chinese) [朱庆勇, 马延文 2000 计算力学学报 17 379]
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[1] Winfree A T 1967 J. Theo. Biol. 16 15
[2] Watts D J 1998 Nature 393 440
[3] Barabási A L, Albert R 1999 Science 286 509
[4] Pecora L M, Carroll T L 1998 Phys. Rev. Lett. 80 2109
[5] Bergner A, Frasca M, Sciuto G, Buscarino A, Ngamga E J,Fortuna L, Kurths J 2012 Phys. Rev. E 85 026208
[6] Kouvaris N, Provata A, Kugiumtzis D 2010 Phys. Lett. A 374 507
[7] Song Q, Cao J D, Liu F 2010 Phys. Lett. A 374 544
[8] Li D, Leyva I, Almendral J A, Sendiña-Nadal I, Buldú J M, Havlin S, Boccaletti S 2008 Phys. Rev. Lett. 101 168701
[9] Donetti L, Hurtado P I, Muñoz M A 2005 Phys. Rev. Lett. 95 188701
[10] Yu W W, Chen G R, L J H 2009 Automatica 45 429
[11] La Rocca C E, Braunstein L A, Macri P A 2009 Phys. Rev. E 80 26111
[12] Selivanov A A, Lehnert J, Dahms T, Hövel P, Fradkov A L, Schöll E 2012 Phys. Rev. E 85 016201
[13] Sun W, Hu T S, Chen Z, Chen S H, Xiao L 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 4501
[14] Jalan S, Amritkar R E 2003 Phys. Rev. Lett. 90 014101
[15] Acebrón J A, Bonilla L L, Vicente C J P, Ritort F, Spigler R 2005 Rev. Mod. Phys. 77 137
[16] Moreno Y, Pacheco A F 2004 Europhys. Lett. 68 603
[17] Cui B T, Lou X Y 2009 Chaos, Solitons and Fractals 39 288
[18] Shang Y, Chen M Y, Kurths J 2009 Phys. Rev. E 80 027201
[19] L L, Li G, Guo L, Meng L, Zou J R, Yang M 2010 Chin. Phys. B 19 080507
[20] Zhu Q Y, Ma Y W 2000 Comput. Mech. 17 379 (in Chinese) [朱庆勇, 马延文 2000 计算力学学报 17 379]
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