Pinning lag synchronization between two dynamical networks with non-derivative and derivative couplings

Li, Zhi-wei   ; Qiu, Zhe-yong   ; Sun, Wei-gang

Kybernetika, Tome 52 (2016) no. 4, pp. 648-660

Abstract (VO)

In this paper, we study lag synchronization between two dynamical networks with non-derivative and derivative couplings via pinning control. We design two types of pinning control schemes, including linear and adaptive feedback controllers. With the corresponding control algorithms, we obtain two theorems on the lag synchronization based on Schur complement and Barbalat's lemma. In addition, we obtain the domain for the linear feedback gains. Finally, we provide two numerical examples to show the efficiency of the proposed schemes and apply random and high-degree chosen pinning schemes.

Détail

DOI : 10.14736/kyb-2016-4-0648

Classification : 05C82, 34D06
Keywords: lag synchronization; pinning control; derivative coupling

Bibliographie

[1] Barabási, A. L., Albert, R.: Emergence of scaling in random networks. Science 286 (1999), 509-512. | DOI | MR | Zbl

[2] Boccaletti, S., Latora, V., Morenoy, Y., Chavez, M., Hwang, D. U.: Complex networks: structure and dynamics. Phys. Rep. 424 (2006), 175-308. | DOI | MR

[3] Boyd, S., Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia 1994. | DOI | MR | Zbl

[4] Chen, T. P., Liu, X. W., Lu, W. L.: Pinning complex networks by a sigle controller. IEEE Trans. Circuits Syst. I 54 (2007), 1317-1326. | DOI | MR

[5] Deng, L. P., Wu, Z. Y., Wu, Q. C.: Pinning synchronization of complex network with non-derivative and derivative coupling. Nonlinear Dyn. 73 (2013), 775-782. | DOI | MR | Zbl

[6] Ding, K., Han, Q. L.: Synchronization of two coupled Hindmarsh-rose neurons. Kybernetika 51 (2015), 784-799. | DOI | MR

[7] Ding, K., Han, Q. L.: Effects of coupling delays on synchronization in Lur'e complex dynamical networks. Int. J. Bifur. Chaos 20 (2010), 3565-3584. | DOI | MR | Zbl

[8] Ding, L., Han, Q. L., Guo, G.: Network-based leader-following consensus for distributed multi-agent systems. Automatica 49 (2013), 2281-2286. | DOI | MR

[9] Dorogovtsev, S. N., Mendes, J. F. F.: Evolution of networks. Adv. Phys. 51 (2002), 1079-1187. | DOI | MR | Zbl

[10] Ge, X. H., Yang, F. W., Han, Q. L.: Distributed networked control systems: A brief overview. Inform. Sci. (2015), in press. | DOI

[11] Gopalsamy, K.: Stability and Oscillation in Delay Differential Equations of Population Differentials. Kluwer Academic, Dordrecht 1992. | DOI | MR

[12] Guo, W. L., Austin, F., Chen, S. H., Sun, W.: Pinning synchronization of complex networks with non-delayed and delayed coupling. Phys. Lett. A 373 (2009), 1565-1572. | DOI | MR

[13] Guo, G., Ding, L., Han, Q. L.: A distributed event-triggered transmission strategy for sampled-data consensus of multi-agent systems. Automatica 60 (2014), 1489-1496. | DOI | MR | Zbl

[14] He, W. L., Zhang, B., Han, Q. L., Qian, F., Kurths, J., Cao, J. D.: Leader-Following Consensus of nonlinear multiagent systems with stochastic sampling. IEEE Trans. Cybernet. (2016), in press. | DOI

[15] Mahbashi, G. A., Noorani, M. S. M., Bakar, S. A.: Projective lag synchronization in drive-response dynamical networks with delay coupling via hybrid feedback control. Nonlinear Dyn. 82 (2015), 1569-1579. | DOI | MR

[16] Mahmoud, E. E., Abualnaja, K. M.: Complex lag synchronization of two identical chaotic complex nonlinear systems. Cent. Eur. J. Phys. 12 (2014), 63-69. | DOI

[17] Newman, M. E. J.: The structure and function of complex networks. SIAM. Rev. 45 (2003), 167-256. | DOI | MR | Zbl

[18] Pecora, L. M., Carroll, T. L.: Master stability functions for synchronized coupled systems. Phys. Rev. Lett. 80 (1998), 2109-2112. | DOI

[19] Santinath, P., Banshidhar, S., Swarup, P.: Generalized lag synchronization of delayed coupled chaotic systems via linear transformations. Phys. Scr. 87 (2013), 045011. | DOI

[20] Shi, H. J., Sun, Y. Z., Miao, L. Y.: Generation of lag synchronization of complex networks with noise coupling. Nonlinear Dyn. 79 (2015), 1131-1140. | DOI | MR

[21] Sun, W., Chen, Z., Lü, Y. B., Chen, S. H.: An intriguing hybrid synchronization phenomenon of two coupled complex networks. Appl. Math. Comput. 216 (2010), 2301-2309. | DOI | MR | Zbl

[22] Sun, W. G., Wang, S., Wang, G. H., Wu, Y. Q.: Lag synchronization via pinning control between two coupled networks. Nonlinear Dyn. 79 (2015), 2659-2666. | DOI | MR

[23] Turci, L. F. R., Macau, E. E. N.: Adaptive node-to-node pinning synchronization control of complex networks. Chaos 22 (2015), 033151. | DOI | MR | Zbl

[24] Wang, X. F., Chen, G. R.: Synchronization in scale-free dynamical networks: robustness and fragility. IEEE Trans. Circuit. Syst. I 49 (2002), 54-62. | DOI | MR

[25] Wu, X. J., Lu, H. T.: Outer synchronization of uncertain general complex delayed networks with adaptive coupling. Neurocomputing 82 (2012), 157-166. | DOI

[26] Wu, J., Sun, Y. Z., Zhao, D. H.: Finite-time adaptive outer synchronization between two complex dynamical networks with nonidentical topological structures. Kybernetika 51 (2015), 655-666. | DOI | MR | Zbl

[27] Xu, Y. H., Zhou, W. N., Fang, J. A., Sun, W.: Adaptive synchronization of the complex dynamical network with non-derivative and derivative coupling. Phys. Lett. A 374 (2010), 1673-1677. | DOI | Zbl

[28] Yu, W. W., Chen, G. R., Lü, J. H.: On pinning synchronization of complex dynamical networks. Automatica 45 (2009), 429-435. | DOI | MR | Zbl

[29] Zheng, S.: Adaptive-impulsive projective synchronization of drive-response delayed complex dynamical networks with time-varying coupling. Nonlinear Dyn. 67 (2012), 2621-2630. | DOI | MR | Zbl

[30] Zheng, S.: Parameter identification and adaptive impulsive synchronization of uncertain complex-variable chaotic systems. Nonlinear Dyn. 74 (2013), 957-967. | DOI | MR | Zbl