Yang, S. S.; Duan, C. K. Generalized synchronization in chaotic systems. (English) Zbl 0946.34040 Chaos Solitons Fractals 9, No. 10, 1703-1707 (1998). Let there be a drive system \(dx/dt=f(x), \;x\in \mathbb{R}^n\), and a function \(H: \mathbb{R}^n \rightarrow \mathbb{R}^m\). The goal is to construct a response system \(dy/dt = g(u(x),y)\) with the drive function \(u\) such that \(||y(t, y_0) - H(x(t,x_0))||\rightarrow 0\) as \(t \rightarrow \infty\) (generalized synchronization). The author proves that the asymptotic stability of the linearized system \(d\eta /dt = g_y (H(x (t,x_0), u(x(t,x_0))))\eta\) implies generalized synchronization. Reviewer: Klaus R.Schneider (Berlin) Cited in 74 Documents MSC: 34C28 Complex behavior and chaotic systems of ordinary differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations Keywords:generalized synchronization; chaotic systems; asymptotic behavior PDFBibTeX XMLCite \textit{S. S. Yang} and \textit{C. K. Duan}, Chaos Solitons Fractals 9, No. 10, 1703--1707 (1998; Zbl 0946.34040) Full Text: DOI References: [1] Pecora, L. M.; Carroll, T. L., Rev. Lett., 64, 821 (1990) [2] Pecora, L. M.; Carroll, T. L., Rev., 44, 2374 (1991) [3] Roy, R.; Scott, K., Rev. Lett., 65, 1575 (1990) [4] Pyragas, K., Phys. Lett., 1992,A170,; Pyragas, K., Phys. Lett., 1992,A170, [5] Maritan, A.; Banavar, J. R., Rev. Lett., 72, 1451 (1994) [6] Winful, H. G.; Rahman, L., Rev. Lett., 65, 1575 (1990) [7] Konh, J. K.; Amritkar, R. E., Rev., 49, 1225 (1994) [8] Cuomo, K. M.; Oppenheim, A. V., Rev. Lett., 71, 65 (1993) [9] Halle, K. S.; Wu, C. W.; Itoh, M.; Chua, L. O., J. Bifurcation Chaos, 3, 469 (1993) [10] Kocarev, L.; Halle, K. S.; Eckert, K.; Chua, L. O.; Parlitz, U., J. Bifurcation Chaos, 3, 479 (1993) [11] Hayes, S.; Grebogi, C.; Ott, E., Rev. Lett., 70, 3031 (1993) [12] Parlitz, U.; Ergezinger, S., Lett., 188, 146 (1994) [13] He, R.; Vaidya, P. G., Rev., 46, 7387 (1992) [14] Kocarev, L.; Parlitz, U., Rev. Lett., 74, 5028 (1995) [15] Peng, J. H.; Ding, E. J.; Ding, M.; Yang, W., Rev. Lett., 76, 904 (1996) [16] Cuomo, K. M.; Oppenheim, A. V., Rev. Lett., 71, 65 (1993) [17] Kocarev, L.; Parlitz, U., Rev. Lett., 76, 1816 (1996) [18] Rössler, O. E., Phys. Lett., 1979,A71,; Rössler, O. E., Phys. Lett., 1979,A71, 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.