zbMATH — the first resource for mathematics

Synchronization in complex networks with non-delay and delay couplings via intermittent control with two switched periods. (English) Zbl 1395.93053
Summary: In this paper, we propose a pinning synchronization control scheme in complex networks with non-delay and delay couplings, which uses two switched periods to provide intermittent control. Criteria ensuring global exponential synchronization are obtained based on strict mathematical proofs. Meanwhile, it is shown that the delay does not depend on the control width and the non-control width. Moreover, we give a method for calculating the minimum number of pinning nodes required to achieve exponential synchronization. Finally, a numerical simulation shows the effectiveness of the pinning synchronization control scheme via an intermittent control method with two periods.

93A14 Decentralized systems
34D06 Synchronization of solutions to ordinary differential equations
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
Full Text: DOI
[1] Strogatz, S. H., Exploring complex networks, Nature, 410, 268-276, (2001) · Zbl 1370.90052
[2] Albert, R.; Barabási, A. L., Statistical mechanics of complex networks, Rev. Modern Phys., 74, 47-97, (2002) · Zbl 1205.82086
[3] Newman, M. E.J., The structure and function of complex networks, SIAM Rev., 45, 167-256, (2003) · Zbl 1029.68010
[4] Wang, X. F.; Chen, G., Complex networks: small-world, scale-free, and beyond, IEEE Circuits Syst. Mag., 3, 1, 6-20, (2003)
[5] Boccaletti, S.; Latora, V.; Moreno, Y.; Chavez, M.; Hwang, D.-U., Complex networks: structure and dynamics, Phys. Rep., 424, 175-308, (2006) · Zbl 1371.82002
[6] Chen, Y.; Lü, J.; Lin, Z., Consensus of discrete-time multi-agent systems with transmission nonlinearity, Automatica, 49, 1768-1775, (2013) · Zbl 1360.93019
[7] Zhu, J.; Lü, J.; Yu, X., Flocking of multi-agent non-holonomic systems with proximity graphs, IEEE Trans. Circuits Syst. I, 60, 199-210, (2013)
[8] Xie, Q.; Chen, G.; Bollt, E. M., Hybrid chaos synchronization and its application in information processing, Math. Comput. Modelling, 35, 145-163, (2002) · Zbl 1022.37049
[9] Lü, J.; Ogorzalek, M. J.; Wang, P., Global relative parameter sensitivities of the feed-forward loops in genetic networks, Neurocomputing, 78, 155-165, (2012)
[10] Pecora, L. M.; Carroll, T. L., Master stability functions for synchronized coupled systems, Phys. Rev. Lett., 80, 2109-2112, (1998)
[11] Zhou, J.; Lu, J. A.; Lü, J. H., Pinning adaptive synchronization of a general complex dynamical network, Automatica, 44, 996-1003, (2008) · Zbl 1283.93032
[12] DeLellis, P.; Bernardo, M.; Garofalo, F., Novel decentralized adaptive strategies for the synchronization of complex networks, Automatica, 45, 1312-1318, (2009) · Zbl 1162.93361
[13] Liu, Y.; Tong, S.; Li, Y., Adaptive neural network tracking control for a class of non-linear systems, Internat. J. Systems Sci., 41, 143-158, (2010) · Zbl 1292.93078
[14] Zhang, H.; Liu, D.; Luo, Y.; Wang, D., Adaptive dynamic programming for control:algorithms and stability, (2013), Springer-Verlag London
[15] Chen, T. P.; Liu, X. W.; Lu, W. L., Pinning complex networks by a single controller, IEEE Trans. Circuits Syst. I, 54, 1317-1326, (2007) · Zbl 1374.93297
[16] Porfiri, M.; Bernardo, M. D., Criteria for global pinning-controllability of complex networks, Automatica, 44, 3100-3106, (2008) · Zbl 1153.93329
[17] Yu, W. W.; Chen, G. R.; Lü, J. H., On pinning synchronization of complex dynamical networks, Automatica, 45, 429-435, (2009) · Zbl 1158.93308
[18] Guo, W. L.; Austin, F.; Chen, S. H., Global synchronization of nonlinearly coupled complex networks with non-delayed and delayed coupling, Commun. Nonlinear Sci. Numer. Simul., 15, 1631-1639, (2010) · Zbl 1221.34213
[19] Wu, X. J.; Lu, H. T., Hybrid synchronization of the general delayed and non-delayed complex dynamical networks via pinning control, Neurocomputing, 89, 168-177, (2012)
[20] Yu, W.; Chen, G.; Lü, J.; Kurths, J., Synchronization via pinning control on general complex networks, SIAM J. Control Optim., 51, 1395-1416, (2013) · Zbl 1266.93071
[21] Zhang, G.; Liu, Z.; Ma, Z., Synchronization of complex dynamical networks via impulsive control, Chaos, 17, 043126, (2007) · Zbl 1163.37389
[22] Wang, Y. W.; Yang, M.; Wang, H. O.; Guan, Z. H., Robust stabilization of complex switched networks with parametric uncertainties and delays via impulsive control, IEEE Trans. Circuits Syst. I, 56, 2100-2108, (2009)
[23] Zhang, H.; Ma, T.; Huang, G.; Wang, Z., Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control, IEEE Trans. Syst. Man Cybern. B, 40, 831-844, (2010)
[24] Yang, X.; Cao, J., Stochastic synchronization of coupled neural networks with intermittent control, Phys. Lett. A, 373, 3259-3272, (2009) · Zbl 1233.34020
[25] Xia, W.; Cao, J., Pinning synchronization of delayed dynamical networks via periodically intermittent control, Chaos, 19, 013120, (2009) · Zbl 1311.93061
[26] Cai, S.; Hao, J.; He, Q.; Liu, Z., Exponential synchronization of complex delayed dynamical networks via pinning periodically intermittent control, Phys. Lett. A, 375, 1965-1971, (2011) · Zbl 1242.05253
[27] Hu, C.; Yu, J.; Jiang, H.; Teng, Z., Exponential synchronization of complex networks with finite distributed delays coupling, IEEE Trans. Neural Netw., 12, 1999-2010, (2011)
[28] Sun, W.; Chen, S. H.; Guo, W. L., Adaptive global synchronization of a general complex dynamical network with non-delayed and delayed coupling, Phys. Lett. A, 372, 6340-6346, (2008) · Zbl 1225.05223
[29] Li, H. J., New criteria for synchronization stability of continuous complex dynamical networks with non-delayed and delayed coupling, Commun. Nonlinear Sci. Numer. Simul., 16, 1027-1043, (2011) · Zbl 1221.34198
[30] Wang, J. L.; Wu, H. N., Local and global exponential output synchronization of complex delayed dynamical networks, Nonlinear Dynam., 67, 497-504, (2012) · Zbl 1242.93008
[31] Zhang, H.; Wang, Z.; Liu, D., Global asymptotic stability of recurrent neural networks with multiple time-varying delays, IEEE Trans. Neural Netw., 19, 855-873, (2008)
[32] Liu, Z.; Zhang, H.; Zhang, Z., Novel stability analysis for recurrent neural networks with multiple delays via line integral-type L-K functional, IEEE Trans. Neural Netw., 21, 1710-1718, (2010)
[33] Fu, J.; Zhang, H.; Ma, T.; Zhang, Q., On passivity analysis for stochastic neural networks with interval time-varying delay, Neurocomputing, 73, 795-801, (2010)
[34] Yu, W.; Cao, J.; Lü, J., Global synchronization of linearly hybrid coupled networks with time-varying delay, SIAM J. Appl. Dyn. Syst., 7, 108-133, (2008) · Zbl 1161.94011
[35] Zochowski, M., Intermittent dynamical control, Physica D, 145, 181-190, (2000) · Zbl 0963.34030
[36] Lü, J.; Yu, X.; Chen, G.; Cheng, D., Characterizing the synchronizability of small-world dynamical networks, IEEE Trans. Circuits Syst. I, 51, 787-796, (2004) · Zbl 1374.34220
[37] Lü, J.; Chen, G., A time-varying complex dynamical network model and its controlled synchronization criteria, IEEE Trans. Automat. Control, 50, 841-846, (2005) · Zbl 1365.93406
[38] Wu, J.; Jiao, L., Synchronization in complex delayed dynamical networks with nonsymmetric coupling, Physica A, 386, 513-530, (2007)
[39] Lütkepohl, H., Handbook of matrices, (1996), Wiley New York · Zbl 0856.15001
[40] Zhou, J.; Chen, T., Synchronization in general complex delayed dynamical networks, IEEE Trans. Circuits Syst. I, 53, 733-744, (2006) · Zbl 1374.37056
[41] Hwang, S. G., Cauchy’s interlace theorem for eigenvalues of Hermitian matrices, Amer. Math. Monthly, 111, 157-159, (2004) · Zbl 1050.15008
[42] Li, D.; Lu, J. A.; Wu, X.; Chen, G. R., Estimating the global basin of attraction and positively invariant set for the Lorenz system and a unified chaotic system, J. Math. Anal. Appl., 323, 2, 844-853, (2006) · Zbl 1104.37024
[43] Lü, J.; Chen, G., A new chaotic attractor coined, Internat. J. Bifur. Chaos, 12, 659-661, (2002) · Zbl 1063.34510
[44] Chen, G.; Ueta, T., Yet another chaotic attractor, Internat. J. Bifur. Chaos, 9, 1465-1466, (1999) · Zbl 0962.37013
[45] Matsumoto, T., A chaotic attractor from chua’s circuit, IEEE Trans. Circuits Syst., CAS-31, 1055-1058, (1984) · Zbl 0551.94020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.