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Cluster synchronization in directed networks of non-identical systems with noises via random pinning control. (English) Zbl 1395.93041

Summary: This paper is concerned with the issue of mean square cluster synchronization in directed networks, which consist of non-identical nodes infected by communication noises. The pinning control method is employed in designing controllers for guaranteeing cluster synchronization, meanwhile, all the controllers are supposed to occur with different probabilities by introducing the Bernoulli stochastic variables. Based on the Lyapunov stability theory and the stochastic theory, the sufficient synchronization conditions are derived and proved theoretically, which are mainly for the controllers to be designed and the noise intensities. Finally, some numerical examples are presented to demonstrate the effectiveness of the results.

MSC:

93A14 Decentralized systems
93E03 Stochastic systems in control theory (general)
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[1] Strogatz, S. H., Exploring complex networks, Nature, 410, 268-276, (2001) · Zbl 1370.90052
[2] Pagani, G. A.; Aiello, M., The power grid as a complex network: a survey, Physica A, 392, 2688-2700, (2013) · Zbl 1395.94418
[3] Tang, J. J.; Wang, Y. H.; Liu, F., Characterizing traffic time series based on complex network theory, Physica A, 392, 4192-4201, (2013)
[4] Wu, J. S.; Wang, X. H.; Jiao, L. C., Synchronization on overlapping community network, Physica A, 391, 508-514, (2012)
[5] Tauro, C. B.; Tamarit, F. A.; Gleiser, P. M., Synchronization in lattice-embedded scale-free networks, Physica A, 391, 834-842, (2012)
[6] Hu, A. H.; Xu, Z. Y.; Guo, L. X., The existence of generalized synchronization of chaotic systems in complex networks, Chaos, 20, 013112, (2010) · Zbl 1311.34114
[7] Batista, C. A.S.; Lameu, E. L.; Batista, A. M.; Lopes, S. R.; Pereira, T.; Zamora-López, G.; Kurths, J.; Viana, R. L., Phase synchronization of bursting neurons in clustered small-world networks, Phys. Rev. E, 86, 016211, (2012)
[8] Kitajima, H.; Yoshihara, T., Cluster synchronization in coupled systems with hub structure, Physica D, 241, 1804-1810, (2012) · Zbl 1259.93023
[9] Singh, A.; Jalan, S., Transition from the self-organized to the driven dynamical clusters, Physica A, 391, 6655-6663, (2012)
[10] Lü, J. H.; Chen, G. R., A time-varying complex dynamical network model and its controlled synchronization criteria, IEEE Trans. Automat. Control, 50, 841-846, (2005) · Zbl 1365.93406
[11] Kaneko, K., Relevance of dynamic clustering to biological networks, Physica D, 75, 55-73, (1994) · Zbl 0859.92001
[12] Cao, J. D.; Li, L. L., Cluster synchronization in an array of hybrid coupled neural networks with delay, Neural Netw., 22, 335-342, (2009) · Zbl 1338.93284
[13] Rulkov, N. F., Images of synchronized chaos: experiments with circuits, Chaos, 6, 262, (1996)
[14] Kouomou, Y. C.; Woafo, P., Cluster synchronization in coupled chaotic semiconductor lasers and application to switching in chaos-secured communication networks, Opt. Commun., 223, 283-293, (2003)
[15] Yu, W. W.; Chen, G. R.; Lü, J. H.; Kurths, J., Synchronization via pinning control on general complex networks, SIAM J. Control Optim., 51, 1395-1416, (2013) · Zbl 1266.93071
[16] Sorrentino, F.; di Bernardo, M.; Garofalo, F.; Chen, G., Controllability of complex networks via pinning, Phys. Rev. E, 75, 046103, (2007)
[17] Su, H. S.; Rong, Z. H.; Chen, M. Z.Q.; Wang, X. F.; Chen, G. R.; Wang, H. W., Decentralized adaptive pinning control for cluster synchronization of complex dynamical networks, IEEE Trans. Cybern., 43, 394-399, (2013)
[18] Wang, Y. L.; Cao, J. D., Cluster synchronization in nonlinearly coupled delayed networks of non-identical dynamic systems, Nonlinear Anal. RWA, 14, 842-851, (2013) · Zbl 1254.93013
[19] Liu, X. W.; Chen, T. P., Cluster synchronization in directed networks via intermittent pinning control, IEEE Trans. Neural Netw., 22, 1009-1020, (2011)
[20] Wang, S. G.; Yao, H. X.; Zheng, S.; Xie, Y., A novel criterion for cluster synchronization of complex dynamical networks with coupling time-varying delays, Commun. Nonlinear Sci. Numer. Simul., 17, 2997-3004, (2012) · Zbl 1243.93038
[21] Liu, Y. Y.; Slotine, J. J.; Barabási, A. L., Controllability of complex networks, Nature, 473, 167-173, (2011)
[22] Tang, Y.; Gao, H. J.; Zou, W.; Kurths, J., Distributed synchronization in networks of agent systems with nonlinearities and random switchings, IEEE Trans. Cybern., 43, 358-370, (2013)
[23] Tang, Y.; Wong, W. K., Distributed synchronization of coupled neural networks via randomly occurring control, IEEE Trans. Neur. Netw. and Learn. Syst., 24, 435-447, (2013)
[24] Li, L. L.; Cao, J. D., Cluster synchronization in an array of coupled stochastic delayed neural networks via pinning control, Neurocomputing, 74, 846-856, (2011)
[25] Wu, X. J.; Lu, H. T., Cluster synchronization in the adaptive complex dynamical networks via a novel approach, Phys. Lett. A, 375, 1559-1565, (2011) · Zbl 1242.05258
[26] Yu, L.; Tu, L. L.; Liu, H. F., Adaptive cluster synchronization for a complex dynamical network with delays and stochastic perturbation, Eur. Phys. J. B, 86, 130, (2013) · Zbl 1515.37050
[27] Chen, Y.; Lü, J. H.; Lin, Z. L., Consensus of discrete-time multi-agent systems with transmission nonlinearity, Automatica, 49, 1768-1775, (2013) · Zbl 1360.93019
[28] Chen, Y.; Lü, J. H.; Han, F. L.; Yu, X. H., On the cluster consensus of discrete-time multi-agent systems, Systems Control Lett., 60, 517-523, (2011) · Zbl 1222.93007
[29] Yu, W. W.; Lellis, P.; Chen, G. R.; Bernardo, M.; Kurths, J., Distributed adaptive control of synchronization in complex networks, IEEE Trans. Automat. Control, 57, 2153-2158, (2012) · Zbl 1369.93321
[30] Wang, J. Y.; Feng, J. W.; Xu, C.; Zhao, Y., Cluster synchronization of nonlinearly-coupled complex networks with nonidentical nodes and asymmetrical coupling matrix, Nonlinear Dynam., 67, 1635-1646, (2012) · Zbl 1242.93009
[31] Khasminskii, R., Stochastic stability of differential equations, (2012), Springer-Verlag Berlin Heidelberg · Zbl 1259.60058
[32] Liu, X. W.; Chen, T. P., Synchronization analysis for nonlinearly-coupled complex networks with an asymmetrical coupling matrix, Physica A, 387, 4429-4439, (2008)
[33] Wang, Y. L.; Cao, J. D., Pinning synchronization of delayed neural networks with nonlinear inner-coupling, Discrete Dyn. Nat. Soc., 2011, 901085, (2011) · Zbl 1234.93006
[34] Porfiri, M.; Fiorilli, F., Experiments on node-to-node pinning control of chua’s circuits, Physica D, 239, 454-464, (2010) · Zbl 1193.37140
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