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Synchronization criteria and pinning control of general complex networks with time delay. (Synchronization criterions and pinning control of general complex networks with time delay.) (English) Zbl 1188.34100

The problem of synchronization for general time-delay complex dynamical networks is investigated. Some new and less conservative conditions are obtained for both continuous-time and discrete-time cases, which guarantee the synchronized states to be asymptotically stable. These conditions are converted to LMIs. Some numerical examples are presented.

MSC:

34K20 Stability theory of functional-differential equations
34K35 Control problems for functional-differential equations
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[1] Strogatz, S. H., Exploring complex networks, Nature, 410, 268-276 (2001) · Zbl 1370.90052
[2] Barabási, A. L.; Albert, R., Emergence of scaling in random networks, Science, 286, 509-512 (1999) · Zbl 1226.05223
[3] Dorogovtesev, S. N.; Mendes, J. F.F., Evolution of networks, Advances in Physics, 51, 1079-1187 (2002)
[4] Newman, M. E.J., The structure and function of complex networks, SIAM Review, 45, 167 (2003) · Zbl 1029.68010
[5] Boccaletti, S.; Latora, V.; Moreno, Y.; Chavez, M.; Hwang, D.-U., Complex networks: structure and dynamics, Physics Reports, 424, 175-308 (2006) · Zbl 1371.82002
[6] Erdös, P.; Rényi, A., On the evolution of random graphs-II, Bulletin of the International Statistical Institute, 38, 343 (1961) · Zbl 0106.12006
[7] Watts, D. J.; Strogatz, S. H., Collective dynamics of small-world networks, Nature, 393, 440-442 (1998) · Zbl 1368.05139
[8] Pecora, L. M.; Carroll, T. L., Master stability functions for synchronized coupled systems, Physics Review Letters, 80, 2109-2112 (1998)
[9] Fink, K. S.; Johnson, G.; Carroll, T.; Mar, D.; Pecora, L., Three coupled oscillator as a universal probe of synchronization stability in coupled oscillator arrays, Physics Review E, 61, 5080 (2000)
[10] Yin, C.; Wang, W.; Chen, G.; Wang, B., Decoupling process for better synchronizability on scale-free networks, Physics Review E, 74, 047102 (2006)
[11] Hong, H.; Kim, B. J.; Choi, M. Y.; Park, H., Factors that predict better synchronizability on complex networks, Physics Review E, 69, 067105 (2004)
[12] Hwang, D.; Chavez, M.; Amann, A.; Boccaletti, S., Synchronization in complex networks with age ordering, Physics Review Letters, 94, 138701 (2005)
[13] Colizza, V.; Banavar, J. R.; Maritan, A.; Rinaldo, A., Network structures from selection principles, Physics Review Letters, 92, 198701 (2004)
[14] Lü, J.; Zhou, T.; Zhang, S., Chaos synchronization between linearly coupled chaotic system, Chaos Solitons & Fractals, 14, 529-541 (2002) · Zbl 1067.37043
[15] Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Physics Review Letters, 64, 821-824 (1990) · Zbl 0938.37019
[16] Albert, R.; Barabási, A. L., Statistical mechanics of complex networks, Review of Modern Physics, 74, 47 (2002) · Zbl 1205.82086
[17] Andrade, J. S.; Bezerra, D. M.; Ribeiro Filho, J.; Moreira, A. A., The complex topology of chemical plants, Physica A, 360, 637-643 (2006)
[18] Donetti, L.; Hurtado, P.; Muñoz, M. A., Entangled networks synchronization and optimal network topology, Physics Review Letters, 95, 188701 (2005)
[19] Chen, M. Y., Synchronization in time-varying networks: a matrix measure approach, Physics Review E, 76, 016104 (2007)
[20] Wang, X. F.; Chen, G., Pinning control of scale-free dynamical networks, Physica A, 310, 521-531 (2002) · Zbl 0995.90008
[21] Wang, X. F.; Chen, G., Synchronization in scale-free dynamical networks: robustness and fragility, IEEE Transactions on Circuits and Systems-I, 49, 54-62 (2002) · Zbl 1368.93576
[22] Wang, X. F.; Chen, G., Synchronization in small-world dynamical networks, International Journal of Bifurcation and Chaos, 9, 1435-1442 (2002)
[23] Li, C. G.; Chen, G., Synchronization in general complex dynamical networks with coupling delays, Physica A, 343, 263-278 (2004)
[24] Wang, L.; Dai, H. P.; Sun, Y. X., Synchronization criteria for a generalized complex delayed dynamical network model, Physica A, 383, 703-713 (2007)
[25] Almaas, E.; Kovács, B.; Vicsek, T.; Oltvai, Z. N.; Barabási, A.-L., Global organization of metabolic fluxes in the bacterium Escherichia coli, Nature, 427, 839-843 (2004)
[26] Gao, H. J.; Lam, J.; Chen, G., New criteria for synchronization stability of general complex dynamical networks with coupling delays, Physica Letter A, 360, 263 (2006) · Zbl 1236.34069
[27] Li, X.; Chen, G., Pinning a complex dynamical networks to its equilibrium, IEEE Transactions on Circuits and Systems-I, 51, 2074-2087 (2004) · Zbl 1374.94915
[28] Liu, Z. X.; Chen, Z. Q.; Yuan, Z. Z., Pinning control of weighted general complex dynamical networks with time delay, Physica A, 375, 345-354 (2007)
[29] Moon, Y. M.; Park, P.; Kwon, W. H.; Lee, Y. S., Delay-dependent robust stabilization of uncertain state-delayed systems, International Journal of Control, 74, 14, 1447-1455 (2001) · Zbl 1023.93055
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