Cluster synchronization for directed heterogeneous dynamical networks via decentralized adaptive intermittent pinning control. (English) Zbl 1348.90152
Summary: In this paper, by proposing a novel adaptive intermittent scheme, we consider the intermittent pinning-control problem for cluster synchronization of directed heterogeneous dynamical networks, i.e., directed networks with nonidentical dynamical nodes. Through constructing a piecewise Lyapunov function and utilizing the analysis technique, some sufficient conditions to guarantee global cluster synchronization are derived. It is noted that the adaptive intermittent strategy developed in this paper is decentralized, which only relies on some local information rather than the global information of the whole network. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.
MSC:
| 90B10 | Deterministic network models in operations research |
| 34D06 | Synchronization of solutions to ordinary differential equations |
| 68M10 | Network design and communication in computer systems |
Keywords:
directed heterogeneous dynamical networks; cluster synchronization; pinning strategy; decentralized adaptive intermittent controlReferences:
| [1] | Strogatz, S.: Exploring complex networks. Nature 410, 268-276 (2001) · Zbl 1370.90052 · doi:10.1038/35065725 |
| [2] | Boccaletti, S., Kurths, J., Osipov, G., Valladares, D.L., Zhou, C.S.: The synchronization of chaotic systems. Phys. Rep. 366, 1-101 (2002) · Zbl 0995.37022 · doi:10.1016/S0370-1573(02)00137-0 |
| [3] | Newman, M.E.J.: The structure and function of complex networks. SIAM Rev. 45, 167-256 (2003) · Zbl 1029.68010 · doi:10.1137/S003614450342480 |
| [4] | Wu, C.: Synchronization in Complex Networks of Nonlinear Dynamical Systems. World Scientific Publishing, Singapore (2007) · Zbl 1135.34002 · doi:10.1142/6570 |
| [5] | Arenas, A., Diaz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C.S.: Synchronization in complex networks. Phys. Rep. 469, 93-153 (2008) · doi:10.1016/j.physrep.2008.09.002 |
| [6] | Li, C., Chen, G.: Phase synchronization in small-world networks of chaotic oscillators. Phys. A 341, 73-79 (2004) · doi:10.1016/j.physa.2004.04.112 |
| [7] | Hu, A., Xu, Z., Guo, L.: The existence of generalized synchronization of chaotic systems in complex networks. Chaos 20, 013112 (2010) · Zbl 1311.34114 · doi:10.1063/1.3309017 |
| [8] | Zhang, Q., Zhao, J.: Projective and lag synchronization between general complex networks via impulsive control. Nonlinear Dyn. 67, 2519-2525 (2012) · Zbl 1243.93011 · doi:10.1007/s11071-011-0164-6 |
| [9] | Ma, Z., Liu, Z., Zhang, G.: A new method to realize cluster synchronization in connected chaotic networks. Chaos 16, 023103 (2006) · Zbl 1146.37330 · doi:10.1063/1.2184948 |
| [10] | Wang, K., Fu, X., Li, K.: Cluster synchronization in community networks with nonidential nodes. Chaos 19, 023106 (2009) · Zbl 1309.34107 · doi:10.1063/1.3125714 |
| [11] | Cao, J., Li, L.: Cluster synchronization in an array of hybrid coupled neural networks with delay. Neural Netw. 22, 335-342 (2009) · Zbl 1338.93284 · doi:10.1016/j.neunet.2009.03.006 |
| [12] | Lu, W., Liu, B., Chen, T.: Cluster synchronization in networks of coupled nonindential dynamical systems. Chaos 20, 013120 (2010) · Zbl 1311.34117 · doi:10.1063/1.3329367 |
| [13] | Zhang, J., Ma, Z., Zhang, G.: Cluster synchronization induced by one-node clusters in networks with asymmetric negative couplings. Chaos 23, 043128 (2013) · Zbl 1331.34118 · doi:10.1063/1.4836710 |
| [14] | 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 |
| [15] | Su, H., Wang, X.: Pinning Control of Complex Networked Systems: Synchronization. Consensus and Flocking of Networked Systems via Pinning. Springer Science and Business Media, Berlin (2013) · Zbl 1366.93002 · doi:10.1007/978-3-642-34578-4 |
| [16] | Chen, T., Liu, X., Lu, W.: Pinning complex networks by a single controller. IEEE Trans. Circuits Syst. I 54, 1317-1326 (2007) · Zbl 1374.93297 · doi:10.1109/TCSI.2007.895383 |
| [17] | Song, Q., Cao, J.: On pinning synchronization of directed and undirected complex dynamical networks. IEEE Trans. Circuits Syst. I 57, 672-680 (2010) · Zbl 1468.93138 · doi:10.1109/TCSI.2009.2024971 |
| [18] | Zhou, J., Lu, J., Lü, J.: Pinning adaptive synchronization of a general complex dynamical network. Automatica 44, 996-1003 (2008) · Zbl 1283.93032 · doi:10.1016/j.automatica.2007.08.016 |
| [19] | Hu, C., Yu, J., Jiang, H., Teng, Z.: Pinning synchronization of weighted complex networks with variable delays and adaptive coupling weights. Nonlinear Dyn. 67, 1373-1385 (2012) · Zbl 1242.93045 · doi:10.1007/s11071-011-0074-7 |
| [20] | Mahdavi, N., Menhaj, M.B., Kurths, J., Lu, J., Afshar, A.: Pinning impulsive synchronization of complex dynamical networks. Int. J. Bifurc. Chaos 22, 1250239 (2012) · Zbl 1258.34127 · doi:10.1142/S0218127412502392 |
| [21] | Lu, J., Kurths, J., Cao, J., Mahdavi, N., Huang, C.: Synchronization control for nonlinear stochastic dynamical networks: pinning impulsive strategy. IEEE Trans. Neural Netw. 23, 285-292 (2012) · doi:10.1109/TNNLS.2011.2179312 |
| [22] | Wu, W., Zhou, W., Chen, T.: Cluster synchronization of linearly coupled complex networks under pinning control. IEEE Trans. Circuits Syst. I (56), 829-839 (2009) · Zbl 1468.93140 · doi:10.1109/TCSI.2008.2003373 |
| [23] | Hu, C., Jiang, H.: Cluster synchronization for directed community networks via pinning partial schemes. Chaos Solitons Fract. 45, 1368-1377 (2012) · Zbl 1258.93068 · doi:10.1016/j.chaos.2012.06.015 |
| [24] | Wang, J., Feng, J., Xu, C., Zhao, Y.: Cluster synchronization of nonlinearly-coupled complex networks with nonidentical nodes and asymmetrical coupling matrix. Nonlinear Dyn. 67, 1635-1646 (2012) · Zbl 1242.93009 · doi:10.1007/s11071-011-0093-4 |
| [25] | Su, H., Rong, Z., Chen, M.Z.Q., Wang, X., Chen, G., Wang, H.: Decentralized adaptive pinning control for cluster synchronization of complex dynamical networks. IEEE Trans. Cybern. 43, 394-399 (2013) · doi:10.1109/TSMCB.2012.2202647 |
| [26] | Wang, Y., Cao, J.: Cluster synchronization in nonlinearly coupled delayed networks of non-identical dynamic systems. Nonlinear Anal.: Real World Appl. 14, 842-851 (2013) · Zbl 1254.93013 · doi:10.1016/j.nonrwa.2012.08.005 |
| [27] | Wu, Z., Fu, X.: Cluster synchronization in community networks with nonidentical nodes via edge-based adaptive pinning control. J. Frankl. Inst. 351, 1372-1385 (2014) · Zbl 1395.93313 · doi:10.1016/j.jfranklin.2013.11.011 |
| [28] | Hu, A., Cao, J., Hu, M., Guo, L.: Cluster synchronization in directed networks of non-identical systems with noises via random pinning control. Phys. A 395, 537-548 (2014) · Zbl 1395.93041 · doi:10.1016/j.physa.2013.10.040 |
| [29] | Li, C., Feng, G., Liao, X.: Stabilization of nonlinear systems via periodically intermittent control. IEEE Trans. Circuits Syst. II (54), 1019-1023 (2007) |
| [30] | Cai, S., Hao, J., He, Q., Liu, Z.: New results on synchronization of chaotic systems with time-varying delays via intermittent control. Nonlinear Dyn. 67, 393-402 (2012) · Zbl 1242.93051 · doi:10.1007/s11071-011-9987-4 |
| [31] | Xia, W., Cao, J.: Pinning synchronization of delayed dynamical networks via periodically intermittent control. Chaos 19, 013120 (2009) · Zbl 1311.93061 · doi:10.1063/1.3071933 |
| [32] | 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 · doi:10.1016/j.physleta.2011.03.052 |
| [33] | Cai, S., Zhou, P., Liu, Z.: Pinning synchronization of hybrid-coupled directed delayed dynamical network via intermittent control. Chaos 24, 033102 (2014) · Zbl 1374.34209 · doi:10.1063/1.4886186 |
| [34] | Hu, C., Jiang, H.: Pinning synchronization for directed networks with node balance via adaptive intermittent control. Nonlinear Dyn. 80, 295-307 (2015) · Zbl 1345.93090 · doi:10.1007/s11071-014-1869-0 |
| [35] | Liu, X., Chen, T.: Cluster synchronization in directed networks via intermittent pinning control. IEEE Trans. Neural Netw. 22, 1009-1020 (2011) · doi:10.1109/TNN.2011.2176769 |
| [36] | Lellis, P., Bernardo, M., Garofalo, F.: Synchronization of complex networks through local adaptive coupling. Chaos 18, 037110 (2008) · Zbl 1309.34090 · doi:10.1063/1.2944236 |
| [37] | Lellis, P., Bernardo, M., Garofalo, F., Porfiri, M.: Evolution of complex networks via edge snapping. IEEE Trans. Circuits Syst. I 57, 2132-2143 (2010) · Zbl 1468.93093 · doi:10.1109/TCSI.2009.2037393 |
| [38] | Rudin, W.: Principles of Mathematical Analysis, 3rd edn. MaGraw-Hill, New York (1976) · Zbl 0346.26002 |
| [39] | Boyd, S., Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994) · Zbl 0816.93004 · doi:10.1137/1.9781611970777 |
| [40] | Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1990) · Zbl 0704.15002 |
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