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Keywords:
synchronization; finite-time; noise perturbation; adaptive feedback controller
Summary:
In this paper, we investigate the finite-time stochastic synchronization problem of two chaotic systems with noise perturbation. We propose new adaptive controllers, with which we can synchronize two chaotic systems in finite time. Sufficient conditions for the finite-time stochastic synchronization are derived based on the finite-time stability theory of stochastic differential equations. Finally, some numerical examples are examined to demonstrate the effectiveness and feasibility of the theoretical results.
References:
[1] 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
[2] Aghababa, M. P., Aghababa, H. P.: A novel finite-time sliding mode controller for synchronization of chaotic systems with input nonlinearity. Arab. J. Sci. Eng. 38 (2013), 3221-3232. DOI 10.1007/s13369-012-0459-z | MR 3116110
[3] Aghababa, M. P., Khanmohammadi, S., Alizadeh, G.: Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique. Appl. Math. Model. 35 (2011), 3080-3091. DOI 10.1016/j.apm.2010.12.020 | MR 2776263 | Zbl 1219.93023
[4] Alvarez, G., Hernández, L., Muñoz, J., Montoya, F., Li, S. J.: Security analysis of communication system based on the synchronization of different order chaotic systems. Phys. Lett. A 345 (2005), 245-250. DOI 10.1016/j.physleta.2005.07.083
[5] Argenti, F., DeAngeli, A., DelRe, E., Genesio, R., Pagni, P., Tesi, A.: Secure communications based on discrete time chaotic systems. Kybernetika 33 (1997), 41-50. MR 1486295
[6] Beran, Z.: On characterization of the solution set in case of generalized semiflow. Kybernetika 45 (2009), 701-715. MR 2599107 | Zbl 1190.93036
[7] Boccaletti, S., Kurths, J., Osipov, G., Valladares, D. L., Zhou, C. S.: The synchronization of chaotic systems. Phys. Rep. 366 (2002), 1-101. DOI 10.1016/s0370-1573(02)00137-0 | MR 1913567 | Zbl 0995.37022
[8] Cai, N., Li, W. Q., Jing, Y. W.: Finite-time generalized synchronization of chaotic systems with different order. Nonlinear Dyn. 64 (2011), 385-393. DOI 10.1007/s11071-010-9869-1 | MR 2803218
[9] Cheng, S., Ji, J. C., Zhou, J.: Fast synchronization of directionally coupled chaotic systems. Appl. Math. Model. 37 (2013), 127-136. DOI 10.1016/j.apm.2012.02.018 | MR 2994171
[10] Čelikovský, S.: Observer form of the hyperbolic-type generalized Lorenz system and its use for chaos synchronization. Kybernetika 40 (2004), 649-664. MR 2120388 | Zbl 1249.93090
[11] Čelikovský, S., Chen, G. R.: On the generalized Lorenz canonical form. Chaos Solition. Fract. 26 (2005), 1271-1276. DOI 10.1016/j.chaos.2005.02.040 | MR 2149315 | Zbl 1100.37016
[12] 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 10.1142/s0218127410027908 | MR 2765079 | Zbl 1208.34082
[13] Ding, K., Han, Q. L.: Master-slave synchronization criteria for horizontal platform systems using time delay feedback control. J. Sound Vibration 330 (2011), 2419-2436. DOI 10.1016/j.jsv.2010.12.006
[14] Ding, K., Han, Q. L.: Master-slave synchronization of nonautonomous chaotic systems and its application to rotating pendulums. Int. J. Bifur. Chaos 22 (2012), 1250147. DOI 10.1142/s0218127412501477 | Zbl 1270.34149
[15] Enjieu, K. H. G., Chabi, O. J. B., Woafo, P.: Synchronization dynamics in a ring of four mutually coupled biological systems. Commun. Nonlinear Sci. Numer. Simul. 13 (2008), 1361-1372. DOI 10.1016/j.cnsns.2006.11.004 | MR 2369467
[16] Grosu, I., Padmanabanm, E., Roy, P. K., Dana, S. K.: Designing coupling for synchronization and amplification of chaos. Phys. Rev. Lett. 100 (2008), 234102. DOI 10.1103/physrevlett.100.234102
[17] He, W. L., Cao, J. D.: Adaptive synchronization of a class of chaotic neural networks with known or unknown parameters. Phys. Lett. A 372 (2008), 408-416. DOI 10.1016/j.physleta.2007.07.050 | Zbl 1217.92011
[18] He, W. L., Du, W. L., Qian, F., Cao, J. D.: Synchronization analysis of heterogeneous dynamical networks. Neurocomputing 104 (2013), 146-154. DOI 10.1016/j.neucom.2012.10.008
[19] He, W. L., Qian, F., Han, Q. L., Cao, J. D.: Synchronization error estimation and controller design for delayed Lur'e systems with parameter mismatches. IEEE Trans. Neur. Net. Lear. Systems 23 (2012), 1551-1563. DOI 10.1109/tnnls.2012.2205941
[20] Henrion, D.: Semidefinite characterisation of invariant measures for one-dimensional discrete dynamical systems. Kybernetika 48 (2012), 1089-1099. MR 3052875 | Zbl 1255.37002
[21] Huang, D. B.: Simple adaptive-feedback controller for identical chaos synchronization. Phys. Rev. E 71 (2005), 037203. DOI 10.1103/physreve.71.037203
[22] Lasalle, J. P.: The extend of asymptotic stability. Proc. Natl. Acad. Sci. U. S. A. 46 (1960), 363-365. DOI 10.1073/pnas.46.3.363 | MR 0113014
[23] 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
[24] 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
[25] Lin, J. S., Yan, J. J.: Adaptive synchronization for two identical generalized Lorenz chaotic systems via a single controller. Nonlinear Anal. Real. 10 (2009), 1151-1159. DOI 10.1016/j.nonrwa.2007.12.005 | MR 2474288 | Zbl 1167.37329
[26] Liu, Y. J.: Circuit implementation and finite-time synchronization of the 4D Rabinovich hyperchaotic system. Nonlinear Dyn. 67 (2012), 89-96. DOI 10.1007/s11071-011-9960-2 | Zbl 1242.93056
[27] Lu, W. L., Chen, T. P.: New approach to synchronization analysis of linearly coupled ordinary differential systems. Physica D 213 (2006), 214-230. DOI 10.1016/j.physd.2005.11.009 | MR 2201200 | Zbl 1105.34031
[28] 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
[29] Mao, X.: Stochastic Differential Equations and Applications. Horwood 1997. Zbl 1138.60005
[30] Ottino, J. M., Muzzio, F. J., Tjahjadi, M., Franjione, J. G., Jana, S. C., Kusch, H. A.: Chaos, symmetry, and self-similarity: exploiting order and disorder in mixing process. Science 257 (1992), 754-760. DOI 10.1126/science.257.5071.754
[31] Pecora, L. M., Carroll, T. L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64 (1990), 821-824. DOI 10.1103/physrevlett.64.821 | MR 1038263 | Zbl 1098.37553
[32] Schiff, S. J., Jerger, K., Duong, D. H., Chang, T., Spano, M. L., Ditto, W. L.: Controlling chaos in the brain. Nature 370 (1994), 615-620. DOI 10.1038/370615a0
[33] Yan, J. J., Hung, M. L., Chiang, T. Y., Yang, Y. Q.: Robust synchronization of chaotic systems via adaptive sliding mode control. Phys. Lett. A 356 (2006), 220-225. DOI 10.1016/j.physleta.2006.03.047 | Zbl 1160.37352
[34] Ma, J., Zhang, A.H., Xia, Y.F., Zhang, L.: Optimize design of adaptive synchronization controllers and parameter observers in different hyperchaotic systems. Appl. Math. Comput. 215 (2010), 3318-3326. DOI 10.1016/j.amc.2009.10.020 | MR 2576820
[35] 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 | Zbl 1242.34078
[36] Wang, H., Han, Z. Z., Xie, Q. Y., Zhang, W.: Finite-time synchronization of uncertain unified chaotic systems based on CLF. Nonlinear Anal. Real. 10 (2009), 2842-2849. DOI 10.1016/j.nonrwa.2008.08.010 | MR 2523247 | Zbl 1183.34072
[37] Yang, Y. Q., Wu, X. F.: Global finite-time synchronization of a class of the non-autonomous chaotic systems. Nonlinear Dyn. 70 (2012), 197-208. DOI 10.1007/s11071-012-0442-y | MR 2991264 | Zbl 1267.93150
[38] Yin, J. L., Khoo, S.: Comments on ``Finite-time stability theorem of stochastic nonlinear systems''. Automatica 47 (2011), 1542-1543. DOI 10.1016/j.automatica.2011.02.052 | MR 2889257
[39] Yin, J. L., Khoo, S., Man, Z. H., Yu, X. H.: Finite-time stability and instability of stochastic nonlinear systems. Automatica 47 (2011), 2671-2677. DOI 10.1016/j.automatica.2011.08.050 | MR 2886936 | Zbl 1235.93254
[40] Zhao, J. K., Wu, Y., Wang, Y. Y.: Generalized finite-time synchronization between coupled chaotic systems of different orders with unknown parameters. Nonlinear Dyn. 74 (2013), 479-485. DOI 10.1007/s11071-013-0970-0 | MR 3117637 | Zbl 1279.34062
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