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Generalized function projective (lag, anticipated and complete) synchronization between two different complex networks with nonidentical nodes. (English) Zbl 1243.93039
Summary: Generalized function projective (lag, anticipated and complete) synchronization between two different complex networks with nonidentical nodes is investigated in this paper. Based on Barbalat’s lemma, some sufficient synchronization criteria are derived by applying the nonlinear feedback control. Although previous work studied function projective synchronization on complex dynamical networks, the dynamics of the nodes are coupled partially linear chaotic systems. In our work, the dynamics of the nodes of the complex networks are any chaotic systems without the limitation of the partial linearity. In addition, each network can be undirected or directed, connected or disconnected, and nodes in either network may have identical or different dynamics. The proposed strategy is applicable to almost all kinds of complex networks. Numerical simulations further verify the effectiveness and feasibility of the proposed synchronization method. Numeric evidence shows that the synchronization rate is sensitively influenced by the feedback strength, the time delay, the network size and the network topological structure.

93B52Feedback control
93C10Nonlinear control systems
93A14Decentralized systems
Full Text: DOI
[1] Strogatz, S. H.: Exploring complex networks, Nature 410, 268-276 (2001)
[2] Horne, A. B.; Hodgman, T. C.; Spence, H. D.; Dalby, A. R.: Constructing an enzyme-centric view of metabolism, Bioinformatics 20, 2050-2055 (2004)
[3] Boccaletti, S.; Latora, V.; Moreno, Y.; Chavezf, M.; Hwanga, D. U.: Complex networks: structure and dynamics, Phys rep 424, 175-308 (2006)
[4] Wu, C. W.: Synchronization in complex networks of nonlinear dynamical systems, (2007) · Zbl 1135.34002
[5] Arenas, A.; Diaz-Guilera, A.; Kurths, J.; Moreno, Y.; Zhou, C.: Synchronization in complex networks, Phys rep 469, 93-153 (2008)
[6] Li, H.: New criteria for synchronization stability of continuous complex dynamical networks with non-delayed and delayed coupling, Commun nonlinear sci numer simulat 16, 1027-1043 (2011) · Zbl 1221.34198 · doi:10.1016/j.cnsns.2010.05.001
[7] Pecora, L. M.; Carroll, T. L.: Master stability functions for synchronized coupled systems, Phys rev lett 80, 2109-2112 (1998)
[8] Wang, X.; Chen, G.: Synchronization in small-world dynamical networks, Int J bifurcat chaos 12, 187-192 (2002)
[9] Wang, X.; Chen, G.: Synchronization in scale-free dynamical networks: robustness and fragility, IEEE trans circuits syst I 49, 54-62 (2002)
[10] Gao, H.; Lam, J.; Chen, G.: New criteria for synchronization stability of general complex dynamical networks with coupling delays, Phys lett A 360, 263-273 (2006) · Zbl 1236.34069
[11] Zhou, J.; Xiang, L.; Liu, Z.: Synchronization in complex delayed dynamical networks with impulsive effects, Physica A 384, 684-692 (2007)
[12] Yu, W.; Chen, G.; Lü, J.: On pinning synchronization of complex dynamical networks, Automatica 45, 429-435 (2009) · Zbl 1158.93308
[13] Wang, Y. W.; Wang, H. O.; Xiao, J. W.; Guan, Z. H.: Synchronization of complex dynamical networks under recoverable attacks, Automatica 46, 197-203 (2010) · Zbl 1214.93101
[14] Li, C. P.; Sun, W. G.; Kurths, J.: Synchronization between two coupled complex networks, Phys rev E 76, 046204 (2007)
[15] Wu, X.; Zheng, W. X.; Zhou, J.: Generalized outer synchronization between complex dynamical networks, Chaos 19, 013109 (2009) · Zbl 1311.34119
[16] Tang, H.; Chen, L.; Lu, J.; Tse, C. K.: Adaptive synchronization between two complex networks with nonidentical topological structures, Physica A 387, 5623-5630 (2008)
[17] Chen, J.; Jiao, L.; Wu, J.; Wang, X.: Adaptive synchronization between two different complex networks with time-varying delay coupling, Chin phys lett 26, 060505 (2009)
[18] Li, Z.; Xue, X.: Outer synchronization of coupled networks using arbitrary coupling strength, Chaos 20, 023106 (2010) · Zbl 1311.34116
[19] Wang, G.; Cao, J.; Lu, J.: Outer synchronization between two nonidentical networks with circumstance noise, Physica A 389, 1480-1488 (2010)
[20] Pecora, L. M.; Carroll, T. L.: Synchronization in chaotic systems, Phys rev lett 64, 821-824 (1990) · Zbl 0938.37019
[21] Kocarev, L.; Parlitz, U.: General approach for chaotic synchronization with applications to communication, Phys rev lett 74, 5028-5031 (1995)
[22] Chen, G.; Dong, X.: From chaos to order: methodologies, perspectives and applications, (1998) · Zbl 0908.93005
[23] Blasius, B.; Huppert, A.; Stone, L.: Complex dynamics and phase synchronization in spatially extended ecological systems, Nature 399, 354-359 (1999)
[24] Wu, X. J.: A new chaotic communication scheme based on adaptive synchronization, Chaos 16, 043118 (2006) · Zbl 1151.94586 · doi:10.1063/1.2401058
[25] Xiao, Y.; Xu, W.; Li, X.; Tang, S.: Adaptive complete synchronization of chaotic dynamical network with unknown and mismatched parameters, Chaos 17, 033118 (2007) · Zbl 1163.37384 · doi:10.1063/1.2759438
[26] Zheng, Z. G.; Hu, G.: Generalized synchronization versus phase synchronization, Phys rev E 62, 7882-7885 (2000)
[27] Rosenblum, M. G.; Pikovsky, A. S.; Kurths, J.: Phase synchronization of chaotic oscillators, Phys rev lett 76, 1804-1807 (1996)
[28] Pikovsky, A. S.; Rosenblum, M. G.; Kurths, J.: From phase to lag synchronization in coupled chaotic oscillators, Phys rev lett 78, 4193-4197 (1997) · Zbl 0896.60090
[29] Voss, H. U.: Anticipating chaotic synchronization, Phys rev E 61, 5115-5119 (2000)
[30] Voss, H. U.: Dynamic long-term anticipation of chaotic states, Phys rev lett 87, 014102 (2001)
[31] Mainieri, R.; Rehacek, J.: Projective synchronization in three-dimensional chaotic systems, Phys rev lett 82, 3042-3045 (1999)
[32] Yan, J.; Li, C.: Generalized projective synchronization of a unified chaotic system, Chaos soliton fract 26, 1119-1124 (2005) · Zbl 1073.65147 · doi:10.1016/j.chaos.2005.02.034
[33] Park, J. H.: Adaptive modified projective synchronization of a unified chaotic system with an uncertain parameter, Chaos soliton fract 34, 1552-1559 (2007) · Zbl 1152.93407 · doi:10.1016/j.chaos.2006.04.047
[34] Li, Z.; Xu, D.: A secure communication scheme using projective chaos synchronization, Chaos soliton fract 22, 477-481 (2004) · Zbl 1060.93530 · doi:10.1016/j.chaos.2004.02.019
[35] Chee, C. Y.; Xu, D.: Secure digital communication using controlled projective synchronization of chaos, Chaos solitons fract 23, 1063-1070 (2005) · Zbl 1068.94010 · doi:10.1016/j.chaos.2004.06.017
[36] Chen, Y.; Li, X.: Function projective synchronization between two identical chaotic systems, Int J mod phys C 18, 883-888 (2007) · Zbl 1139.37301 · doi:10.1142/S0129183107010607
[37] Du, H.; Zeng, Q.; Wang, C.: Modified function projective synchronization of chaotic system, Chaos soliton fract 42, 2399-2404 (2009) · Zbl 1198.93011 · doi:10.1016/j.chaos.2009.03.120
[38] Sudheer, K. Sebastian; Sabir, M.: Modified function projective synchronization of hyperchaotic systems through open-plus-closed-loop coupling, Phys lett A 374, 2017-2023 (2010) · Zbl 1236.34072
[39] Hu, M.; Yang, Y.; Xu, Z.; Zhang, R.; Guo, L.: Projective synchronization in drive-response dynamical networks, Physica A 381, 457-466 (2007)
[40] Zheng, S.; Bi, Q.; Cai, G.: Adaptive projective synchronization in complex networks with time-varying coupling delay, Phys lett A 373, 1553-1559 (2009) · Zbl 1228.05267 · doi:10.1016/j.physleta.2009.03.001
[41] Wu, X.; Lu, H.: Generalized projective synchronization between two different general complex dynamical networks with delayed coupling, Phys lett A 374, 3932-3941 (2010) · Zbl 1237.05196
[42] Feng, C. F.; Xu, X. J.; Wang, S. J.; Wang, Y. H.: Projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks, Chaos 18, 023117 (2008) · Zbl 1307.34076
[43] Zhang, R.; Yang, Y.; Xu, Z.; Hu, M.: Function projective synchronization in drive-response dynamical network, Phys lett A 374, 3025-3028 (2010) · Zbl 1237.34034
[44] Solís-Perales, G.; Ruiz-Velázquez, E.; Valle-Rodríguez, D.: Synchronization in complex networks with distinct chaotic nodes, Commun nonlinear sci numer simulat 14, 2528-2535 (2009) · Zbl 1221.34148 · doi:10.1016/j.cnsns.2008.09.019
[45] Du, H.: Function projective synchronization in drive-response dynamical networks with non-identical nodes, Chaos soliton fract 44, 510-514 (2011) · Zbl 1223.93041 · doi:10.1016/j.chaos.2011.04.002
[46] Li, C.; Chen, G.: Synchronization in general complex dynamical networks with coupling delays, Physica A 343, 263-278 (2004)
[47] Jiang, Y.: Globally coupled maps with time delay interactions, Phys lett A 267, 342-349 (2000)
[48] Masoller, C.; Martí, A. C.; Zanette, D. H.: Synchronization in an array of globally coupled maps with delayed interactions, Physica A 325, 186-191 (2003) · Zbl 1026.37023 · doi:10.1016/S0378-4371(03)00197-3
[49] Earl, M. G.; Strogatz, S. H.: Synchronization in oscillator networks with delayed coupling: a stability criterion, Phys rev E 67, 36204 (2003)
[50] Atay, F. M.; Jost, J.; Wende, A.: Delays, connection topology, and synchronization of coupled chaotic maps, Phys rev lett 92, 144101 (2004)
[51] Masoller, C.; Martí, A. C.: Random delays and the synchronization of chaotic maps, Phys rev lett 94, 134102 (2005)
[52] Chen, M.; Han, Z.: Controlling and synchronizing chaotic Genesio system via nonlinear feedback control, Chaos soliton fract 17, 709-716 (2003) · Zbl 1044.93026 · doi:10.1016/S0960-0779(02)00487-3
[53] Park, J. H.: Controlling chaotic systems via nonlinear feedback control, Chaos soliton fract 23, 1049-1054 (2005) · Zbl 1061.93508 · doi:10.1016/j.chaos.2004.06.016
[54] Chen, H. H.; Sheu, G. J.; Lin, Y. L.; Chen, C. S.: Chaos synchronization between two different chaotic systems via nonlinear feedback control, Nonlinear anal theory methods appl 70, 4393-4401 (2009) · Zbl 1171.34324 · doi:10.1016/j.na.2008.10.069
[55] Khalil, H. K.: Nonlinear systems, (2002) · Zbl 1003.34002
[56] Lü, J.; Chen, G.: A new chaotic attractor coined, Int J bifurcat chaos 12, 659-661 (2002) · Zbl 1063.34510 · doi:10.1142/S0218127402004620
[57] Liu, C. X.; Liu, T.; Liu, L.; Liu, K.: A new chaotic attractor, Chaos soliton fract 22, 1031-1038 (2004) · Zbl 1060.37027
[58] Chen, G.; Ueta, T.: Yet another chaotic attractor, Int J bifurcat chaos 9, 1465-1466 (1999) · Zbl 0962.37013 · doi:10.1142/S0218127499001024
[59] Barabási, A. L.; Albert, R.: Emergence of scaling in random networks, Science 286, 509-512 (1999) · Zbl 1226.05223 · doi:10.1126/science.286.5439.509
[60] Lü, J. H.; Chen, G. R.; Cheng, D. Z.; Celikovsky, S.: Bridge the gap between the Lorenz system and the Chen system, Int J bifurcat chaos 12, 2917-2926 (2002) · Zbl 1043.37026 · doi:10.1142/S021812740200631X