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Lag synchronization of complex networks via pinning control. (English) Zbl 1223.93057
Summary: This paper mainly investigates the lag synchronization of complex networks via pinning control. Without assuming the symmetry and irreducibility of the coupling matrix, sufficient conditions of lag synchronization are obtained by adding controllers to a part of nodes. Particularly, the following two questions are solved: (1) How many controllers are needed to pin a coupled complex network to a homogeneous solution? (2) How should we distribute these controllers? Finally, a simple example is provided to demonstrate the effectiveness of the theory.

93C15Control systems governed by ODE
93A14Decentralized systems
93C10Nonlinear control systems
Full Text: DOI
[1] Carroll, T. L.; Heagy, J. F.; Pecora, L. M.: Transforming signals with chaotic synchronization, Phys. rev. E 54, 4676-4680 (1996)
[2] Rosenblum, M.; Pikovsky, A.; Kurtz, J.: Phase synchronization of chaotic oscillators, Phys. rev. Lett. 76, 1804-1807 (1996)
[3] Pikovsky, A. S.; Rosenblum, M. G.; Osipov, G. V.; Kurths, J.: Phase synchronization of chaotic oscillators by external driving, Physica D 104, 219-238 (1997) · Zbl 0898.70015 · doi:10.1016/S0167-2789(96)00301-6
[4] Mainieri, R.; Rehacek, J.: Projective synchronization in three-dimensional chaotic systems, Phys. rev. Lett. 82, 3042-3045 (1999)
[5] Morgul, O.; Solak, E.: Observer based synchronization of chaotic systems, Phys. rev. E 54, 4803-4811 (1996)
[6] Morgul, O.; Solak, E.: On the synchronization of chaotic systems by using state observers, Int. J. Bifur. chaos 7, 1307-1322 (1997) · Zbl 0967.93509 · doi:10.1142/S0218127497001047
[7] Rosenblum, M.; Pikovsky, A.; Kurtz, J.: From phase to lag synchronization in coupled chaotic oscillator, Phys. rev. Lett. 78, 4193-4196 (1997)
[8] Wu, L.; Zhu, S.: Coexistence and switching of anticipating synchronization and lag synchronization in an optical system, Phys. lett. A 315, 101-108 (2003)
[9] Heil, T.; Fischer, I.; Elsässer, W.; Mulet, J.; Mirasso, C. R.: Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers, Phys. rev. Lett. 86, 795-798 (2001)
[10] Ciszak, M.; Calvo, O.; Masoller, C.; Mirasso, C. R.; Toral, R.: Anticipating the response of excitable systems driven by random forcing, Phys. rev. Lett. 90, 204102 (2003) · Zbl 1026.92014
[11] Ciszak, M.; Marino, F.; Toral, R.; Balle, S.: Dynamical mechanism of anticipating synchronization in excitable systems, Phys. rev. Lett. 93, 114102 (2004)
[12] Corron, N. J.; Blakely, J. N.; Pethel, S. D.: Lag andanticipating synchronization without time-delay coupling, Chaos 15, 023110 (2005)
[13] Shahverdiev, E. M.; Sivaprakasam, S.; Shore, K. A.: Lag synchronization in time-delayed systems, Phys. lett. A 292, 320-324 (2002) · Zbl 0979.37022 · doi:10.1016/S0375-9601(01)00824-6
[14] Li, C.; Liao, X.; Wong, K.: Chaotic lag synchronization of coupled time-delayed systems and its applications in secure communication, Physica D 194, 187-202 (2004) · Zbl 1059.93118 · doi:10.1016/j.physd.2004.02.005
[15] Zhou, J.; Chen, T.; Xiang, L.: Chaotic lag synchronization of coupled delayed neural networks and its applications in secure communication, Circuits systems signal process. 24, 599-613 (2005) · Zbl 1102.94010 · doi:10.1007/s00034-005-2410-y
[16] Sun, Y.; Cao, J.: Adaptive lag synchronization of unknown chaotic delayed neural networks with noise perturbation, Phys. lett. A 364, 277-285 (2007) · Zbl 1203.93110 · doi:10.1016/j.physleta.2006.12.019
[17] Yu, W.; Cao, J.: Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification, Phys. A 375, 467-482 (2007)
[18] Wang, X.; Chen, G.: Pinning control of scale-free dynamical networks, Phys. A 310, 521-531 (2002) · Zbl 0995.90008 · doi:10.1016/S0378-4371(02)00772-0
[19] Li, X.; Wang, X.; Chen, G.: Pinning a complex dynamical networks to its equilibrium, IEEE trans. Circ syst. I 51, 2074-2087 (2004)
[20] Chen, T.; Liu, X.: Pinning complex networks by a single controller, IEEE trans. Circ syst. I 54, 1317-1326 (2007)
[21] Guo, W.; Austin, F.; Chen, S.; Sun, W.: Pinning synchronization of the complex networks with non-delayed and delayed coupling, Phys. lett. A 373, 1565-1572 (2009) · Zbl 1228.05266 · doi:10.1016/j.physleta.2009.03.003
[22] Lu, W.; Chen, T.: New approch to synchronization analysis of linearly coupled ordinary differential systems, Physica D 213, 214-230 (2006) · Zbl 1105.34031 · doi:10.1016/j.physd.2005.11.009