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Keywords:
complex dynamic networks; synchronization; time delay; noise perturbation
Summary:
In this paper, the finite-time stochastic outer synchronization and generalized outer synchronization between two complex dynamic networks with time delay and noise perturbation are studied. Based on the finite-time stability theory, sufficient conditions for the finite-time outer synchronization are obtained. Numerical examples are examined to illustrate the effectiveness of the analytical results. The effect of time delay and noise perturbation on the convergence time are also numerically demonstrated.
References:
[1] Arenas, A., Kurths, J., Moreno, Y., Zhou, C. S.: Synchronization in complex networks. Phys. Rep. 469 (2008), 93-153. DOI 10.1016/j.physrep.2008.09.002 | MR 2477097
[2] Asheghan, M. M., Míguez, J., Hamidi-Beheshti, M. T., Tavazoe, M. S.: Robust outer synchronization between two complex networks with fractional order dynamics. Chaos 21 (2011), 033121. DOI 10.1063/1.3629986 | MR 3388455
[3] Barabasi, A. L.: Scal-free networks: a decade and beyond. Science 325 (2009), 412-413. DOI 10.1126/science.1173299 | MR 2548299
[4] Barabasi, A. L., Albert, R.: Emergence of scaling in random networks. Science 286 (1999), 509-512. DOI 10.1126/science.286.5439.509 | MR 2091634 | Zbl 1226.05223
[5] Blat, S. P., Bernstein, D. S.: Finite-time stability of continuous autonomous systems. SIAM. J. Control Optim. 38 (2000), 751-766. DOI 10.1137/s0363012997321358 | MR 1756893
[6] Guo, W. L., Austin, F., Chen, S.H.: Global synchronization of nonlinearly coupled complex networks with non-delayed and delayed coupling. Commun. Nonlinear Sci. Numer. Simulat. 15 (2010), 1631-1639. DOI 10.1016/j.cnsns.2009.06.016 | MR 2576789 | Zbl 1221.34213
[7] Hardy, G., Littlewood, J., Polya, G.: Inequalities. Cambridge University Press 1988. MR 0944909 | Zbl 0634.26008
[8] Hauschildt, B., Jason, N. B., Balanov, A., Scholl, E.: Noise-induced cooperative dynamics and its control in coupled neuron models. Phys. Rev. E 74 (2006), 051906. DOI 10.1103/physreve.74.051906 | MR 2293732
[9] Huang, J. J., Li, C. D., Huang, T. W., He, X.: Finite-time lag synchronization of delayed neural networks. Neurocomputing 139 (2013), 145-149. DOI 10.1016/j.neucom.2014.02.050
[10] Huang, X. Q., Lin, W., Yang, B.: Global finite-time synchronization of a class of uncertain nonlinear systems. Automatica 41 (2005), 881-888. DOI 10.1016/j.automatica.2004.11.036 | MR 2157720
[11] Kazanovich, Y. B., Borisyuk, R. M.: Synchronization in a neural network of phase oscillators with the central element. Biological Cybernetics 71 (1994), 177-185. DOI 10.1007/s004220050080 | MR 1347145 | Zbl 0804.92002
[12] Kloeden, P. E., Platen, E.: Numerical Solution of Stochastic Differential Equations. Springer, Heidelberg 1992. DOI 10.1007/978-3-662-12616-5 | MR 1214374 | Zbl 1216.60052
[13] Korniss, G.: Synchronization in weighted unccorrelated complex networks in a noisy environment: optimization and connections with transport efficiency. Phys. Rev. E 75 (2007), 051121. DOI 10.1103/physreve.75.051121
[14] Li, H. Y., Hu, Y. A., Wang, R. Q.: Adaptive finite-time synchronization of cross-strict feedback hyperchaotic systems with parameter uncertainties. Kybernetika 49 (2013), 554-567. MR 3117914
[15] Li, L., Kurths, J., Peng, H., Yang, Y., Luo, Q.: Exponentially asymptotic synchronization of uncertain complex time-delay dynamical networks. The European Physical Journal B 86 (2013), 1-9. DOI 10.1140/epjb/e2013-30517-6 | MR 3082432
[16] Lin, W., Chen, G. R.: Using white noise to enhance synchronization of coupled chaotic systems. Chaos 16 (2006), 013134. DOI 10.1063/1.2183734 | MR 2220550 | Zbl 1144.37375
[17] Lü, J. H., Yu, X. H., Chen, G. R.: Chaos synchronization of general complex dynamical networks. Physica A 334 (2004), 281-302. DOI 10.1016/j.physa.2003.10.052 | MR 2044940
[18] Lynnyk, V., Čelikovský, S.: On the anti-synchronization detection for the generalized Lorenz system and its applications to secure encryption. Kybernetika 46 (2010), 1-18. MR 2666891 | Zbl 1190.93038
[19] 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. Simulat. 18 (2013), 2462-2478. DOI 10.1016/j.cnsns.2012.11.009 | MR 3042052 | Zbl 1311.34157
[20] Nagail, K. H., Kori, H.: Noise-induced synchronization of a large population of globally coupled nonidentical oscillators. Phys. Rev.E 81 (2010), 065202. DOI 10.1103/physreve.81.065202
[21] Pecora, L. M., Carrol, T. L.: Master stability functions for synchronized coupled system. Phys. Rev. Lett. 80 (1998), 2109-2112. DOI 10.1103/physrevlett.80.2109
[22] 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
[23] Sun, Y. Z., Li, W., Ruan, J.: Generalized outer synchronization between complex dynamic networks with time delay and noise perturbation. Commun. Nonliear Sci. Numer. Simul. 18 (2013), 989-998. DOI 10.1016/j.cnsns.2012.08.040 | MR 2996611
[24] Sun, F., Peng, H., Luo, Q., Li, L., Yang, Y.: Parameter identification and projective synchronization between different chaotic systems. Chaos 19 (2009), 023109. DOI 10.1063/1.3127599 | MR 2548749 | Zbl 1309.34106
[25] Sun, Y. Z., Ruan, J.: Synchronization in coupled time-delayed systems with parameter mismath and noise perturbation. Chaos 19 (2009), 043113. DOI 10.1063/1.3262488
[26] Sun, Y. Z., Shi, H. J., Bakare, E. A., Meng, Q. X.: Noise-induced outer synchronization between two different complex dynamical networks. Nonlinear Dyn. 76 (2014), 519-528. DOI 10.1007/s11071-013-1145-8 | MR 3189189 | Zbl 1319.37028
[27] Tang, H. W., Chen, L., Lu, J. A., Tse, C. K.: Adaptive synchronization between two nonidentical topological structures. Physica A 387 (2008), 5623-5630. DOI 10.1016/j.physa.2008.05.047
[28] Wang, G. J., Cao, J. D., Lu, J. Q.: Outer synchronization between two nonidentical networks with circumstance noise. Physica A 389 (2010), 1480-1488. DOI 10.1016/j.physa.2009.12.014
[29] Wang, X. F., Chen, G. R.: Synchronization in scal-free dynamical networks: robustness and fragility. IEEE Trans. Circuits Syst. I 49 (2002), 54-62. DOI 10.1109/81.974874 | MR 1874226
[30] Wang, H., Han, Z. Z., Xie, Q. Y., Zhang, W.: Finite-time synchronization of uncertain unified chaotic systems based on CLF. Nonlinear Anal.: Real World Appl. 10 (2009), 2842-2849. DOI 10.1016/j.nonrwa.2008.08.010 | MR 2523247 | Zbl 1183.34072
[31] Wang, H., Han, Z. Z., Xie, Q. Y., Zhang, W.: Finite-time chaos control via nonsingular terminal sliding model control. Commun. Nonlinear Sci. Numer. Simulat. 14 (2012), 2728-2733. DOI 10.1016/j.cnsns.2008.08.013 | MR 2483882
[32] Wang, W., Li, L., Peng, H., Xiao, J., Yang, Y.: Synchronization control of memristor-based recurrent neural networks with perturbations. Neural Networks. 53 (2014), 8-14. DOI 10.1016/j.neunet.2014.01.010 | Zbl 1307.93038
[33] Wang, W. P., Peng, H. P., Li, L. X., Xiao, J. H., Yang, Y. X.: Finite-time function projective synchronization in complex multi-links networks with time-varying delay. Neural Process. Lett. 41 (2015), 71-88. DOI 10.1007/s11063-013-9335-4
[34] Watts, D. J., Strogatz, S. H.: Collective dynamics of small-world networks. Nature 393 (1998), 440-442. DOI 10.1038/30918
[35] Yang, X. S., Cao, J. D.: Finite-time stochastic synchronization of complex networks. App. Math. Modeling. 34 (2010), 3631-3641. DOI 10.1016/j.apm.2010.03.012 | MR 2651795 | Zbl 1201.37118
[36] Yu, W. W., Chen, G. R., Lü, J. H.: On pinning synchronization of complex dynamical networks. Zbl 1158.93308
[37] Zhou, X. B., Jiang, M. R., Huang, Y. Q.: Switched modified function projective synchronization between two complex nonlinear hyperchaotic systems based on adaptive control and parameter identification. Kybernetika 50 (2014), 632-642. DOI 10.14736/kyb-2014-4-0632 | MR 3275089 | Zbl 1311.34120
[38] Zhou, C. S., Motter, A. E., Kurths, J.: Universality in the synchronization of weighted random networks. Phys. Rev. Lett. 96 (2006), 034101. DOI 10.1103/physrevlett.96.034101
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