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Chaos synchronization between complex networks with uncertain structures and unknown parameters

Zhang Meng Lü Ling Lü Na Fan Xin

Chaos synchronization between complex networks with uncertain structures and unknown parameters

Zhang Meng, Lü Ling, Lü Na, Fan Xin
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  • Chaos synchronization between complex networks with uncertain structures and unknown parameters is investigated. By designing appropriate control inputs, we achieve the synchronization between two complex networks. The unknown parameters of nodes at two networks and the coupling strength between the nodes are identified simultaneously in the process of synchronization. The CO2 laser equation with modulation loss is taken for example to simulate experiment. It is found that the synchronization performance between two networks is very stable.
    • Funds: Project supported by the Natural Science Foundation of Liaoning Province, China(Grant No. 20082147), and the Innovative Team Program of Liaoning Educational Committee, China (Grant No. 2008T108).
    [1]

    Ji D H, Park J H, Yoo W J, Won S C, Lee S M 2010 Phys. Lett. A 374 1218

    [2]

    Kouvaris N, Provata A, Kugiumtzis D 2010 Phys. Lett. A 374 507

    [3]

    Agnes E J, Erichsen Jr R, Brunnet L G 2010 Physica A 389 651

    [4]

    Li K, Lai C H 2008 Phys. Lett. A 372 1601

    [5]

    Hung Y C, Huang Y T, Ho M C, Hu C K 2008 Phys. Rev. E 77 16202

    [6]

    He G M, Yang J Y 2008 Chaos, Solitons and Fractal 38 1254

    [7]

    Checco P, Biey M, Kocarev L 2008 Chaos, Solitons and Fractals 35 562

    [8]

    Pisarchik A N, Jaimes-Reátegui R, Sevilla-Escoboza R, Boccaletti S 2009 Phys. Rev. E 79 55202

    [9]

    Chen L, Qiu C, Huang H B 2009 Phys. Rev. E 79 45101

    [10]

    Li D, Leyva I, Almendral J A, Sendiña-Nadal I, Buldú J M, Havlin S, Boccaletti S 2008 Phys. Rev. Lett. 101 168701

    [11]

    Posadas-Castillo C, Cruz-Hernández C, López-Gutiérrez R M 2009 Chaos, Solitons and Fractals 40 1963

    [12]

    Yu W W, Chen G R, Lü J H 2009 Automatica 45 429

    [13]

    Solis-Perales G, Ruiz-Velázquez E, Valle-Rodriguez D 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 2528

    [14]

    La Rocca C E, Braunstein L A, Macri P A 2009 Phys. Rev. E 80 26111

    [15]

    Shang Y, Chen M Y, Kurths J 2009 Phys. Rev. E 80 27201

    [16]

    Emura T 2006 Phys. Lett. A 349 306

    [17]

    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]

    [18]

    Selivanov A A, Lehnert J, Dahms T, Hövel P, Fradkov A L, Schöll E 2012 Phys. Rev. E 85 016201

    [19]

    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)]

    [20]

    Lü L, Cao H J 2003 Opt. Tech. 29 89 (in Chinese) [吕翎, 曹海静2003光学技术 29 89]

  • [1]

    Ji D H, Park J H, Yoo W J, Won S C, Lee S M 2010 Phys. Lett. A 374 1218

    [2]

    Kouvaris N, Provata A, Kugiumtzis D 2010 Phys. Lett. A 374 507

    [3]

    Agnes E J, Erichsen Jr R, Brunnet L G 2010 Physica A 389 651

    [4]

    Li K, Lai C H 2008 Phys. Lett. A 372 1601

    [5]

    Hung Y C, Huang Y T, Ho M C, Hu C K 2008 Phys. Rev. E 77 16202

    [6]

    He G M, Yang J Y 2008 Chaos, Solitons and Fractal 38 1254

    [7]

    Checco P, Biey M, Kocarev L 2008 Chaos, Solitons and Fractals 35 562

    [8]

    Pisarchik A N, Jaimes-Reátegui R, Sevilla-Escoboza R, Boccaletti S 2009 Phys. Rev. E 79 55202

    [9]

    Chen L, Qiu C, Huang H B 2009 Phys. Rev. E 79 45101

    [10]

    Li D, Leyva I, Almendral J A, Sendiña-Nadal I, Buldú J M, Havlin S, Boccaletti S 2008 Phys. Rev. Lett. 101 168701

    [11]

    Posadas-Castillo C, Cruz-Hernández C, López-Gutiérrez R M 2009 Chaos, Solitons and Fractals 40 1963

    [12]

    Yu W W, Chen G R, Lü J H 2009 Automatica 45 429

    [13]

    Solis-Perales G, Ruiz-Velázquez E, Valle-Rodriguez D 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 2528

    [14]

    La Rocca C E, Braunstein L A, Macri P A 2009 Phys. Rev. E 80 26111

    [15]

    Shang Y, Chen M Y, Kurths J 2009 Phys. Rev. E 80 27201

    [16]

    Emura T 2006 Phys. Lett. A 349 306

    [17]

    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]

    [18]

    Selivanov A A, Lehnert J, Dahms T, Hövel P, Fradkov A L, Schöll E 2012 Phys. Rev. E 85 016201

    [19]

    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)]

    [20]

    Lü L, Cao H J 2003 Opt. Tech. 29 89 (in Chinese) [吕翎, 曹海静2003光学技术 29 89]

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  • Received Date:  18 April 2012
  • Accepted Date:  28 May 2012
  • Published Online:  20 November 2012

Chaos synchronization between complex networks with uncertain structures and unknown parameters

  • 1. College of Physics and Electronic Technology, Liaoning Normal University, Dalian 116029, China
Fund Project:  Project supported by the Natural Science Foundation of Liaoning Province, China(Grant No. 20082147), and the Innovative Team Program of Liaoning Educational Committee, China (Grant No. 2008T108).

Abstract: Chaos synchronization between complex networks with uncertain structures and unknown parameters is investigated. By designing appropriate control inputs, we achieve the synchronization between two complex networks. The unknown parameters of nodes at two networks and the coupling strength between the nodes are identified simultaneously in the process of synchronization. The CO2 laser equation with modulation loss is taken for example to simulate experiment. It is found that the synchronization performance between two networks is very stable.

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