Vincent, U. E.; Guo, R. Finite-time synchronization for a class of chaotic and hyperchaotic systems via adaptive feedback controller. (English) Zbl 1242.34078 Phys. Lett., A 375, No. 24, 2322-2326 (2011). Summary: This Letter investigates chaos synchronization of chaotic and hyperchaotic systems. Based on finite-time stability theory, a simple adaptive control method for realizing chaos synchronization in a finite time is proposed. In comparison with previous methods, the present method is not only simple, but could also be easily utilized in application. Numerical simulations are given to illustrate the effectiveness and validity of the proposed approach. Cited in 31 Documents MSC: 34C28 Complex behavior and chaotic systems of ordinary differential equations 34D06 Synchronization of solutions to ordinary differential equations 34H10 Chaos control for problems involving ordinary differential equations 34K20 Stability theory of functional-differential equations 93C40 Adaptive control/observation systems 93B52 Feedback control Keywords:chaos; finite-time synchronization; chaos synchronization; hyperchaotic system; adaptive feedback control PDFBibTeX XMLCite \textit{U. E. Vincent} and \textit{R. Guo}, Phys. Lett., A 375, No. 24, 2322--2326 (2011; Zbl 1242.34078) Full Text: DOI References: [1] Pecora, L. M.; Carroll, T. L., Phys. Rev. Lett., 64, 821 (1990) [2] Boccaletti, S.; Grebogi, C.; Lai, Y. C., Phys. Rep., 329, 103 (2000) [3] Boccaletti, S.; Kurths, J.; Osipov, G.; Valladares, D. L., Phys. Rep., 366, 1 (2002) [4] Ojalvo, J.; Roy, R., Phys. Rev. Lett., 86, 5204 (2001) [5] Murali, K.; Lakshmanan, M., Phys. Rev. E, 49, 4882 (1994) [6] Yang, T.; Chua, L., IEEE Trans. Circ. Syst., 44, 976 (1997) [7] Bowong, S., Phys. Lett. A, 326, 102 (2004) [8] Heagl, J. F.; Carroll, T. L.; Pecora, L. M., Phys. Rev. E, 52, R1253 (1995) [9] Shuai, J. W.; Wong, K. W.; Cheng, L. M., Phys. Rev. E, 56, 2272 (1997) [10] S. Bhat, D. Bernstein, in: Proceedings of ACC, Albuquerque, NM, 1997, p. 2513.; S. Bhat, D. Bernstein, in: Proceedings of ACC, Albuquerque, NM, 1997, p. 2513. [11] Haimo, V. T., SIAM J. Control Optim., 24, 760 (1986) [12] Yu, W., Phys. Lett. A, 374, 3021 (2010) [13] Millerioux, G.; Mira, C., IEEE Trans. Circ. Syst. Fund. Theor. Appl., 48, 111 (2001) [14] Li, S.; Tian, Y.-P., Chaos Solitons Fractals, 15, 303 (2003) [15] Perruquetti, W.; Floquet, T.; Moulay, E., IEEE Trans. Automat. Control, 53, 356 (2008) [16] Wang, H.; Han, Z. Z., Commun. Nonlinear Sci. Numer. Simul., 14, 2239 (2009) [17] Wang, H.; Han, Z. Z., Nonlinear Anal. Real World Appl., 10, 2842 (2009) [18] Yang, X.; Cao, J., Appl. Math. Model., 34, 3631 (2010) [19] Guo, R. W., Phys. Lett. A, 372, 5593 (2008) · Zbl 1223.34078 [20] Vincent, U. E.; Guo, R., Commun. Nonlinear Sci. Numer. Simul., 14, 3925 (2009) [21] Guo, R.; Vincent, U. E.; Idowu, B. A., Phys. Scripta, 79, 035801 (2009) [22] Corron, N. J.; Pethel, S. D.; Hopper, B. A., Phys. Rev. Lett., 84, 3835 (2000) [23] Hilker, F. M., Phys. Rev. E, 73, 052901 (2006) [24] Vincent, U. E., Acta Phys. Polon. B, 38, 2459 (2007) [25] Guo, R.; Vincent, U. E., Chin. Phys. Lett., 26, 090506 (2009) [26] Yu, W., Phys. Lett. A, 374, 1488 (2010) [27] Guo, R.; Vincent, U. E., Phys. Lett. A, 375, 119 (2010) [28] Genesio, R.; Tesi, A., Automatica, 28, 531 (1992) [29] Ito, K., Earth Planet. Sci. Lett., 51, 451 (1980) [30] Lü, J. H.; Chen, G. R.; Cheng, D. Z., Int. J. Bifur. Chaos, 12, 2917 (2002) [31] Tigan, G.; Opris, D., Chaos Solitons Fractals, 36, 1315 (2008) [32] Chen, A.; Lu, J.; Lü, J.; Yu, S., Physica A, 364, 103 (2006) [33] Wang, F. Q.; Liu, C. X., Chin. J. Phys., 15, 0963 (2006) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.