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Keywords:
complex networks; outer synchronization; finite-time; adaptive feedback controllers
Summary:
In this paper, we investigate the finite-time adaptive outer synchronization between two complex dynamical networks with nonidentical topological structures. We propose new adaptive controllers, with which we can synchronize two complex dynamical networks within finite time. Sufficient conditions for the finite-time adaptive outer synchronization are derived based on the finite-time stability theory. Finally, numerical examples are examined to demonstrate the effectiveness and feasibility of the theoretical results.
References:
[1] An, X. L., Zhang, L., Li, Y. Z., Zhang, J. G.: Synchronization analysis of complex networks with multi-weights and its application in public traffic network. Physica A: Statist. Mech. Appl. 412 (2014), 149-156. DOI 10.1016/j.physa.2014.06.033 | MR 3237793
[2] Aghababa, M. P., Aghababa, H. P.: A general nonlinear adaptive control scheme for finite-time synchronization of chaotic systems with uncertain parameters and nonlinear inputs. Nonlinear Dyn. 69 (2012), 1903-1914. DOI 10.1007/s11071-012-0395-1 | MR 2945528 | Zbl 1263.93111
[3] Aghababa, M. P., Aghababa, H. P.: Adaptive finite-time synchronization of non-autonomous chaotic systems with uncertainty. J. Comput. Nonlin. Dyn. 8 (2013), 031006. DOI 10.1115/1.4023007
[4] Chen, D. Y., Zhang, R. F., Liu, X. Z., Ma, X. Y.: Fractional order Lyapunov stability theorem and its applications in synchronization of complex dynamical networks. Commun. Nonlinear Sci. Numer. Simul. 19 (2014), 4105-4121. DOI 10.1016/j.cnsns.2014.05.005 | MR 3215040
[5] Dimassi, H., Loría, A., Belghith, S.: A new secured transmission scheme based on chaotic synchronization via smooth adaptive unknown-input observers. Commun. Nonlinear Sci. Numer. Simul. 17 (2012), 3727-3739. DOI 10.1016/j.cnsns.2012.01.024 | Zbl 1258.94010
[6] Genesio, R., Tesi, A.: Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems. Automatica 28 (1992), 531-548. DOI 10.1016/0005-1098(92)90177-h | Zbl 0765.93030
[7] Guirey, E., Bees, M. A., Martin, A., Srokosz, M.: Persistence of cluster synchronization under the influence of advection. Phys. Rev. E 81 (2010), 1511-1521. DOI 10.1103/physreve.81.051902 | MR 2736247
[8] He, P., Ma, S. H., Fan, T.: Finite-time mixed outer synchronization of complex networks with coupling time-varying delay. Chaos 22 (2012), 043151. DOI 10.1063/1.4773005 | MR 3388713
[9] Huberman, B. A., Adamic, L. A.: Internet-Growth dynamics of the world-wide web. Nature 401 (1999), 6749, 131. DOI 10.1038/43604
[10] Lasalle, J. P.: The extend of asymptotic stability. Proc. Natl. Acad. Sci. USA 46 (1960), 363-365. DOI 10.1073/pnas.46.3.363 | MR 0113014
[11] Lasalle, J. P.: Some extensions of Liapunov's second method. IRE Trans. Circuit Theory 7 (1960), 520-527. DOI 10.1109/tct.1960.1086720 | MR 0118902
[12] Li, C. G., Chen, G. R.: Synchronization of networks with coupling delays. Phys. A: Statist. Mech. Appl. 343 (2004), 263-278. DOI 10.1016/j.physa.2004.05.058
[13] Li, C. P., Sun, W. G., Kurths, J.: Synchronization between two coupled complex networks. Phys. Rev. E 76 (2007), 046204. DOI 10.1103/physreve.76.046204
[14] Liao, T. L., Huang, N. S.: An observer-based approach for chaotic synchronization with applications to secure communications. IEEE Trans. Circuits Syst. I 46 (1999), 1144-1150. DOI 10.1109/81.788817 | Zbl 0963.94003
[15] 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
[16] Mei, J., Jiang, M. H., Xu, W. M., Wang, B.: Finite-time synchronization control of complex dynamical networks with time delay. Commun. Nonlinear Sci. Numer. Simul. 18 (2013), 2462-2478. DOI 10.1016/j.cnsns.2012.11.009 | MR 3042052 | Zbl 1311.34157
[17] Revayova, M., Torok, C.: Piecewise approximation and neural networks. Kybernetika 43 (2007), 547-559. MR 2377932 | Zbl 1145.68495
[18] Strogatz, S. H., Stewart, I.: Coupled oscillators and biological synchronization. Sci. Am. 269 (1993), 102-109. DOI 10.1038/scientificamerican1293-102
[19] Sun, W., Chen, Z., Kang, Y. H.: Impulsive synchronization of a nonlinear coupled complex network with a delay node. Chin. Phys. B 21 (2012), 010504. DOI 10.1088/1674-1056/21/1/010504
[20] Sun, W. G., Li, S. X.: Generalized outer synchronization between two uncertain dynamical networks. Nonlinear Dyn. 77 (2014), 481-489. DOI 10.1007/s11071-014-1311-7 | MR 3229176 | Zbl 1314.34121
[21] Sun, Y. Z., Li, W., Ruan, J.: Finite-time generalized outer synchronization between two different complex networks. Commun. Theor. Phys. 58 (2012), 697-703. DOI 10.1088/0253-6102/58/5/13 | MR 3089102 | Zbl 1264.05128
[22] Sun, Y. Z., Li, W., Ruan, J.: Generalized outer synchronization between two complex dynamical networks with time delay and noise perturbation. Commun. Nonlinear Sci. Numer. Simul. 18 (2013), 989-998. DOI 10.1016/j.cnsns.2012.08.040 | MR 2996611
[23] Sun, Y. Z., Li, W., Zhao, D. H.: Finite-time stochastic outer synchronization between two complex dynamical networks with different topologies. Chaos 22 (2012), 023152. DOI 10.1063/1.4731265 | MR 3388569
[24] Sun, W. G., Wu, Y. Q., Zhang, J. Y., Qin, S.: Inner and outer synchronization between two coupled networks with interactions. J. Franklin Inst. 352 (2015), 3166-3177. DOI 10.1016/j.jfranklin.2014.08.004 | MR 3369921
[25] 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 10.1007/s11071-014-1838-7 | MR 3317469
[26] Tan, S. L., Lü, J. H., Yu, X. H., Hill, D. J.: Evolution and maintenance of cooperation via inheritance of neighborhood relationship. Chin. Sci. Bull. 58 (2013), 28 - 29, 3491-3498. DOI 10.1007/s11434-013-5984-y
[27] Tan, S. L., Lü, J. H., Hill, D. J.: Towards a theoretical framework for analysis and intervention of random drift on general networks. IEEE Trans. Automat. Control 60 (2015), 2, 576-581. DOI 10.1109/tac.2014.2329235 | MR 3310190
[28] Vincent, U. E., Guo, R.: Finite-time synchronization for a class of chaotic and hyperchaotic systems via adaptive feedback controller. Phys. Lett. A 375 (2011), 2322-2326. DOI 10.1016/j.physleta.2011.04.041 | MR 2737904
[29] Watts, D. J., Strogatz, S. H.: Collective dynamics of ‘small-world’ networks. Nature 393 (1998), 440-442. DOI 10.1038/30918
[30] Wong, Y. C., Sundareshan, M. K.: A simplex trained neural network-based architecture for sensor fusion and tracking of target maneuvers. Kybernetika 35 (1999), 613-636. MR 1728471 | Zbl 1274.93265
[31] Wu, Z. Y., Fu, X. C.: Outer synchronization between drive-response networks with nonidentical nodes and unknown parameters. Nonlinear Dyn. 69 (2012), 685-692. DOI 10.1007/s11071-011-0296-8 | MR 2929902 | Zbl 1258.34131
[32] Wu, Z. G., Park, J. H., Su, H. Y., Chu, J.: Discontinuous Lyapunov functional approach to synchronization of time-delay neural networks using sampled-data. Nonlinear Dyn. 69 (2012), 102-109. DOI 10.1007/s11071-012-0404-4 | MR 2945537 | Zbl 1263.34075
[33] Wu, Z. Y., Ye, Q. L., Liu, D. F.: Finite-time synchronization of dynamical networks coupled with complex-variable chaotic systems. Int. J. Mod. Phys. C 24 (2013), 1350058. DOI 10.1142/s0129183113500587 | MR 3103796
[34] Yang, X. S., Cao, J. D., Lu, J. Q.: Synchronization of delayed complex dynamical networks with impulsive and stochastic effects. Nonlinear Anal., Real World Appl. 12 (2011), 2252-2266. DOI 10.1016/j.nonrwa.2011.01.007 | MR 2801017 | Zbl 1223.37115
[35] Yang, X., Wu, Z. Y., Cao, J. D.: Finite-time synchronization of complex networks with nonidentical discontinuous nodes. Nonlinear Dyn. 73 (2013), 2313-2327. DOI 10.1007/s11071-013-0942-4 | MR 3094795 | Zbl 1281.34100
[36] Zheng, C., Cao, J. D.: Finite-time synchronization of the singular hybrid coupled networks. J. Appl. Math. 2013 (2013), 378376. DOI 10.1155/2013/378376 | MR 3045405
[37] Zhong, W. S., Stefanovski, J. D., Dimirovski, G. M., Zhao, J.: Decentralized control and synchronization of time-varying complex dynamical network. Kybernetika 45 (2009), 151-167. MR 2489586 | Zbl 1158.34332
[38] Zhou, J., Lu, J. A., Lü, J. H.: Adaptive synchronization of an uncertain complex dynamical network. IEEE Trans. Automat. Control 51 (2006), 4, 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), 4, 996-1003. DOI 10.1016/j.automatica.2007.08.016 | MR 2530942 | Zbl 1158.93339
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