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Keywords:
complex dynamical network; pinning control; directed coupling; time delay; DCN oscillator
complex dynamical network; pinning control; directed coupling; time delay; DCN oscillator
Summary:
The primary objective of the present paper is to develop an approach for analyzing pinning synchronization stability in a complex delayed dynamical network with directed coupling. Some simple yet generic criteria for pinning such coupled network are derived analytically. Compared with some existing works, the primary contribution is that the synchronization manifold could be chosen as a weighted average of all the nodes states in the network for the sake of practical control tactics, which displays the different influences and contributions of the various nodes in synchronization seeking processes of the dynamical network. Furthermore, it is shown that in order to drive a complex network to a desired synchronization state, the coupling strength should vary according to the controller. In addition, the theoretical results about the time-invariant network is extended to the time-varying network, and the result on synchronization problem can also be extended to the consensus problem of networked multi-agent systems. Subsequently, the theoretic results are illustrated by a typical scale-free (SF) neuronal network. Numerical simulations with three kinds of the homogenous solutions, including an equilibrium point, a periodic orbit, and a chaotic attractor, are finally given to demonstrate the effectiveness of the proposed control methodology.
References:
[1] Arenas, A., Diaz-Guilera, A., Kurths, J., Morenob, Y., Zhoug, C.: Synchronization in complex networks. Phys. Rep. 469 (2008), 93-153. DOI 10.1016/j.physrep.2008.09.002 | MR 2477097
[2] Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U.: Complex networks: structure and dynamics. Phys. Rep. 424 (2006), 175-308. DOI 10.1016/j.physrep.2005.10.009 | MR 2193621
[3] Cai, S. M., Zhou, J., Xiang, L., Liu, Z. R.: Robust impulsive synchronization of complex delayed dynamical networks. Phys. Lett. A 372 (2008), 4990-4995. DOI 10.1016/j.physleta.2008.05.077 | Zbl 1221.34075
[4] Cai, S. M., He, Q. B., Hao, J. J., Liu, Z. R.: Exponential synchronization of complex networks with nonidentical time-delayed dynamical nodes. Phys. Lett. A 374 (2010), 2539-2550. DOI 10.1016/j.physleta.2010.04.023 | MR 2640029 | Zbl 1236.05185
[5] Chen, T. P., Liu, X. W., Lu, W. L.: Pinning complex networks by a single controller. IEEE Trans. Circuits Syst. I. Reg. Pap. 54 (2007), 1317-1326. DOI 10.1109/tcsi.2007.895383 | MR 2370589
[6] Chen, Y., Lü, J. H., Yu, X. H., Lin, Z. L.: Consensus of discrete-time second-order multiagent systems based on infinite products of general stochastic matrices. SIAM J. Control Optim. 51 (2013), 3274-3301. DOI 10.1137/110850116 | MR 3090151 | Zbl 1275.93005
[7] Chen, Y., Lü, J. H., Lin, Z. L.: Consensus of discrete-time multi-agent systems with transmission nonlinearity. Automatica 49 (2013), 1768-1775. DOI 10.1016/j.automatica.2013.02.021 | MR 3049226
[8] Guo, W. L., Austin, F., Chen, S. H., Sun, W.: Pinning synchronization of the complex networks with non-delayed and delayed coupling. Phys. Lett. A 373 (2009), 1565-1572. DOI 10.1016/j.physleta.2009.03.003 | MR 2513417 | Zbl 1228.05266
[9] Li, Z., Lee, J. J.: New eigenvalue based approach to synchronization in asymmetrically coupled networks. Chaos 17 (2007), 043117-043117. DOI 10.1063/1.2804525 | MR 2380036 | Zbl 1163.37347
[10] Li, X., Wang, X. F., Chen, G. R.: Pinning a complex dynamical network to its equilibrium. IEEE Trans. Circuits Syst. I. Reg. Pap. 51 (2004), 2074-2087. DOI 10.1109/tcsi.2004.835655 | MR 2096915
[11] Liang, H. T., Wang, Z., Yue, Z. M., Lu, R. H.: Generallized synchronization and control for incommensurate fractional unified chaotic system and applications in secure communication. Kybernetika 48 (2012), 190-205. MR 2954320
[12] Liu, B., Lu, W. L., Chen, T. P.: Pinning consensus in networks of multiagents via a single impulsive controller. IEEE Trans. Neural Netw. Learn. Syst. 24 (2013), 1141-1149. DOI 10.1109/tnnls.2013.2247059
[13] Lu, H. T.: Chaotic attractors in delayed neural networks. Phys. Lett. A 298 (2002), 109-116. DOI 10.1016/s0375-9601(02)00538-8 | Zbl 0995.92004
[14] Lu, W. L.: Adaptive dynamical networks via neighborhood information: synchronization and pinning control. Chaos 17 (2007), 023122-023122. DOI 10.1063/1.2737829 | MR 2340616 | Zbl 1159.37366
[15] Lu, W. L., Chen, T. P.: New approach to synchronization analysis of linearly coupled ordinary differential systems. Phys. D 213 (2006), 214-230. DOI 10.1016/j.physd.2005.11.009 | MR 2201200 | Zbl 1105.34031
[16] Lu, S. J, Chen, L.: A general synchronization method of chaotic communication system via kalman filtering. Kybernetika 44 (2008), 43-52. MR 2405054
[17] Lu, J. Q., Wang, Z. D., Cao, J. D., Ho, D. W. C., Kurths, J.: Pinning impulsive stabilization of nonlinear dynamical networks with time-varying delay. Int. J. Bifurc. Chaos 22 (2012), 1250176-1250176. DOI 10.1142/s0218127412501763 | Zbl 1270.92006
[18] Lü, J. H., Yu, X., Chen, G. R., Cheng, D. Z.: Characterizing the synchronizability of small-world dynamical networks. IEEE Trans. Circuits Syst. I. Reg. Pap. 51 (2004), 787-796. DOI 10.1109/tcsi.2004.823672 | MR 2066214
[19] Lü, J. H., Yu, X., Chen, G. R.: Chaos synchronization of general complex dynamical networks. Phys. A 334 (2004), 281-302. DOI 10.1016/j.physa.2003.10.052 | MR 2044940
[20] Lü, J. H., Chen, G. R.: A time-varying complex dynamical network model and its controlled synchronization criteria. IEEE Trans. Automat. Control 50 (2005), 841-846. DOI 10.1109/tac.2005.849233 | MR 2142000
[21] Ma, M. H., Zhang, H., Cai, J. P., Zhou, J.: Impulsive practical synchronization of n-dimensional nonautonomous systems with parameter mismatch. Kybernetika 49 (2013), 539-553. MR 3117913 | Zbl 1274.70039
[22] Porfiri, M., Bernardo, M. di: Criteria for global pinning-controllability of complex networks. Automatica 44 (2008), 3100-3106. DOI 10.1016/j.automatica.2008.05.006 | MR 2531411 | Zbl 1153.93329
[23] Porfiri, M., Fiorilli, F.: Node-to-node pinning control of complex networks. Chaos 19 (2009), 013122-013122. DOI 10.1063/1.3080192 | MR 2513766
[24] Song, Q., Cao, J. D.: On pinning synchronization of directed and undirected complex dynamical networks. IEEE Trans. Circuits Syst. I. Reg. Pap. 57 (2010), 672-680. DOI 10.1109/tcsi.2009.2024971 | MR 2729966
[25] Sorrentino, F., Bernardo, M., Garofalo, F., Chen, G. R.: Controllability of complex networks via pinning. Phys. Rev. E 75 (2007), 046103-046103. DOI 10.1103/physreve.75.046103
[26] Tang, Y., Wang, Z. D., Fang, J A.: Pinning control of fractional-order weighted complex networks. Chaos 19 (2009), 013112-013112. DOI 10.1063/1.3068350 | MR 2513760
[27] Wang, X. F., Chen, G. R.: Synchronization in scale-free dynamical networks: robustness and fragility. IEEE Trans. Circuits Syst. I. Fundam. Theory Appl. 49 (2002), 54-62. DOI 10.1109/81.974874 | MR 1874226
[28] Wang, X. F., Chen, G. R.: Synchronization in small-world dynamical networks. Int. J. Bifurc. Chaos 12 (2002), 187-192. DOI 10.1142/s0218127402004292
[29] Wang, X. F., Chen, G. R.: Pinning control of scale-free dynamical networks. Phys. A 310 (2002), 521-531. DOI 10.1016/s0378-4371(02)00772-0 | MR 1946327 | Zbl 0995.90008
[30] Wu, Y. Y., Wei, W., Li, G. Y., Xiang, J.: Pinning control of uncertain complex networks to a homogeneous orbit. IEEE Trans. Circuits Syst. II Exp. Briefs 56 (2009), 235-239. DOI 10.1109/tcsii.2009.2015350
[31] Wu, W., Zhou, W. J., Chen, T. P.: Cluster synchronization of linearly coupled complex networks under pinning control. IEEE Trans. Circuits Syst. I. Reg. Pap. 56 (2009), 829-839. DOI 10.1109/tcsi.2008.2003373 | MR 2724977
[32] Xia, W. G., Cao, J. D.: Pinning synchronization of delayed dynamical networks via periodically intermittent control. Chaos 19 (2009), 013120-013120. DOI 10.1063/1.3071933 | MR 2513764
[33] Xiang, J., Chen, G. R.: Analysis of pinning-controlled networks: a renormalization approach. IEEE Trans. Automat. Control 54 (2009), 1869-1875. DOI 10.1109/tac.2009.2020668 | MR 2552820
[34] Xiang, L. Y., Liu, Z. X., Chen, Z. Q., Chen, F., Yuan, Z. Z.: Pinning control of complex dynamical networks with general topology. Phys. A 379 (2007), 298-306. DOI 10.1016/j.physa.2006.12.037
[35] Xiang, L. Y., Zhu, J. J. H.: On pinning synchronization of general coupled networks. Nonlin. Dynam. 64 (2011), 339-348. DOI 10.1007/s11071-010-9865-5 | MR 2803214
[36] Yu, W. W., Chen, G. R., Lü, J. H.: On pinning synchronization of complex dynamical networks. Automatica 45 (2009), 429-435. DOI 10.1016/j.automatica.2008.07.016 | MR 2527339 | Zbl 1158.93308
[37] Zhou, J., Chen, T. P.: Synchronization in general complex delayed dynamical networks. IEEE Trans. Circuits Syst. I. Reg. Pap. 53 (2006), 733-744. DOI 10.1109/tcsi.2005.859050 | MR 2212426
[38] Zhou, J., Lu, J. A., Lü, J. H.: Adaptive synchronization of an uncertain complex dynamical network. IEEE Trans. Automat. Control 51 (2006), 652-656. DOI 10.1109/tac.2006.872760 | MR 2228029
[39] Zhou, J., Lu, J. A., Lü, J. H.: Pinning adaptive synchronization of a general complex dynamical network. Automatica 44 (2008), 996-1003. DOI 10.1016/j.automatica.2007.08.016 | MR 2530942 | Zbl 1158.93339
[40] Zhou, J., Wu, Q. J., Xiang, L.: Pinning complex delayed dynamical networks by a single impulsive controller. IEEE Trans. Circuits Syst. I. Reg. Pap. 58 (2011), 2882-2893. DOI 10.1109/tcsi.2011.2161363 | MR 2907084
[41] Zhou, J., Wu, Q. J., Xiang, L.: Impulsive pinning complex dynamical networks and applications fo firing neuronal synchronization. Nonlin. Dynam. 69 (2012), 1393-1403. DOI 10.1007/s11071-012-0355-9 | MR 2943393
[42] Zhou, J., Wu, Q. J., Xiang, L., Cai, S. M., Liu, Z. R.: Impulsive synchronization seeking in complex delayed dynamical networks. Nonlin. Anal.: Hybrid Syst. 5 (2011), 513-524. DOI 10.1016/j.nahs.2010.10.013 | MR 2819260
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