[1] Ott, E. [1993], Chaos in Dynamical Systems, Cambridge Cambridge, University Press.

[2] Thompson, J. M. T., H. B. Stewart [1986], Nonlinear Dynamics and Chaos, Chichester, Wiley.

[3] Schuster, H. G. [1988], Deterministic Chaos, 2nd éd., Weinheim, VHC Publishers.

[4] Bergé, P., Y. Pomeau, C. Vidal [1984], Order within Chaos: Towards a Deterministic Approach to Turbulence, New York, John Wiley and Sons.

[5] Moon, F. C. [1992], Chaotic and Fractal Dynamics, New York, John Wiley and Sons.

[6] Gaponov-Grekhov, A. V., M. I. Rabinovich, [1992], Nonlinearities in Action -Oscillations, Chaos, Order, Fractals, Berlin, Springer.

[7] Lauterborn, W., J. Holzfuss, [1991], "Acoustic chaos"\ Int. J. Bifurcation and Chaos, 1, 13-26.

[8] Lauterborn, W., U. Parlitz, [1988], "Methods of chaos physics and their application to acoustics'', J. Acoust. Soc. Am., 84,1975-1993.

[9] Abarbanel, H.D.I., R. Brown, J.J. Sidorowich, L.SH. Tsimring, [1993], "The analysis of observed chaotic data in physical systems", Rev. Mod. Phys., 65, 1331-1392.

[10] Guckenheimer, J., P. Holmes, [1983], Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, New York, Springer.

[11] Feigenbaum, M. J., [1978], "Quantitative universality for a class of nonlinear transformations", J. Stat. Phys., 19, 25-52.

[12] Lauterborn, W., T. Kurz, M. Wiesenfeldt, [1995] Coherent Optics, Berlin, Springer.

[13] Mettin, R., U. Parlitz, W. Lauterborn, [1993], "Bifurcation structure of the driven van der Pol oscillator", Int. J. Bifurcation and Chaos, 3, 1529-1555.

[14] Packard, N.H., J.P. Crutchfield, J.D. Farmer, R.S. Shaw [1980], "Geometry from a time series", Phys. Rev. Lett., 45, 712-716.

[15] Takens, F. [1981], "Detecting strange attractors in turbulence", in Dynamical Systems and Turbulence, eds. Rand, D.A. & Young, L.-S., Berlin, Springer, 366-381. 14

[16] Sauer, T., Y. Yorke, M. Casdagli [1991], "Embedology", J. Stat. Phys., 65, 579-616.

[17] Sauer, T., J.A. Yorke [1993], "How many delay coordinates do you need ?", Int. J. Bifurcation and Chaos, 3, 737-744.

[18] Casdagli, M., S. Eubank, J.D. Farmer, J. Gibson [1991], "State space reconstruction in the presence of noise", Physica A 51, 52-98.

[19] Gibson, J.F., J.D. Farmer, M. Casdagli, S. Eubank [1992], "An analytic approach to practical state space reconstruction" Physica D, 57,1-30.

[20] Sauer, T.[1994], "Reconstruction of dynamical systems from interspike intervals", Phys. Rev. Lett., 72, 3811-3814.

[21] Cenys, A., K. Pyragas [1988], "Estimation of the number of degrees of freedom from chaotic time series", Phys. Lett. A,129, 227-230.

[22] Buzug, Th., T. Reimers, G. Pfister [1990], "Optimal reconstruction of strange Attractors from purely geometrical arguments", Europhys. Lett., 13, 605-610.

[23] Alecsic, Z. [1991], "Estimating the embedding dimension", Physica D, 52, 362-368.

[24] Buzug, Th., G. Pfister [1992], "Optimal delay time and embedding dimension for delaytime coordinates by analysis of the global static and local dynamical behavior of strange attractors", Phys. Rev. A, 45, 7073-7084.

[25] Gao, J., Z. Zheng [1993], "Local exponential divergence plot and optimal embedding of a chaotic time series", Phys. Lett. A, 181, 153-158.

[26] Gao, J., Z. Zheng [1994], "Direct dynamical test for deterministic chaos and optimal embedding of a chaotic time series", Phys. Rev. E, 49, 3807-3814.

[27] Huerta, R., C. Santa Cruz, J.R. Dorronsore, V. Lopez [1995], "Local state-space reconstruction using averaged scalar products of dynamical-system flow vectors", Europhys. Lett., 29, 13-18.

[28] Liebert, W., K. Pawelzik, H.G. Schuster [1991], "Optimal embeddings of chaotic attractors from topological considerations", Europhys. Lett., 14, 521-526.

[29] Kennel, M.B., R. Brown, H.D.I. Abarbanel [1992], "Determining embedding dimension for phase-space reconstruction using a geometrical construction", Phys. Rev. A, 45, 3403-3411.

[30] Kember, G., A.C. Fowler [1993], "A correlation function for choosing time delays in phase portrait reconstructions", Phys. Lett. A, 179, 72-80.

[31] Rosenstein, M.T., J.J. Collins, C.J. De Luca [1994], "Reconstruction expansion as a geometry-based framework for choosing proper dealy times", Physica D, 73, 82-98.

[32] Frazer, A.M., H.L. Swinney [1986], "Independent coordinates in strange attractors from mutual information", Phys. Rev. A, 33, 1134-1140.

[33] Frazer, A.M. [1989], "Reconstructing attractors from scalar time series: a comparison of singular system and redundancy criteria", Physica D, 34, 391-404.

[34] Frazer, A.M. [1989], "Information and entropy in strange attractors", IEEE Trans. Info. Theory, 35, 245-262. 15

[35] Liebert, W., H.G. Schuster [1989], "Proper choice of the time delay for the analysis of chaotic time series", Phys. Lett. A, 142,107-111.

[36] Martinerie, J.M., A.M. Albano, A.I. Mees, P.E. Rapp [1992], "Mutual information, strange attractors, and the optimal estimation of dimension", Phys. Rev. A, 45, 7058-7064.

[37] Broomhead, D.S., G.P. King [1986], "Extracting qualitative dynamics from experimental data", Physica D, 20, 217-236.

[38] Landa, P.S., M.G. Rosenblum [1991], "Time series analysis for system identification and diagnostics", Physica D, 48, 232-254.

[39] Palus, M., I. Dvorak [1992], "Singular-value decomposition in attractor reconstruction: pitfalls and precautions", Physica D, 55, 221-234.

[40] Farmer, J.D., J.J. Sidorowich [1987], "Predicting chaotic time series", Phys. Rev. Lett., 59, 845-848.

[41] Casdagli, M. [1989], "Nonlinear Prediction of chaotic time series", Physica D, 35, 335-356.

[42] Brown, R. N.F. Rulkov, E.R. Tracy [1994], "Modeling and synchronizing chaotic systems from time-series data", Phys. Rev. E, 49, 3784-3800.

[43] Grassberger, P., T. Schreiber, C. Schaffrath [1991], "Nonlinear time sequence analysis", Int. J. Bifurcation and Chaos, 1, 521-547.

[44] Grassberger, P., I. Procaccia [1983], "On the characterization of of strange attractors", Phys. Rev. Lett., 50, 346-349.

[45] Theiler, J. [1986], "Spurious dimension from correlation algorithms applied to limited time-series data", Phys. Rev. A, 34, 2427-2431.

[46] Badii, R., A. Politi [1984], "Hausdorff dimension and uniformity factor of strange attractors", Phys. Rev. Lett, 52,1661-1664.

[47] Badii, R., A. Politi [1985], "Statistical description of chaotic attractors", J. stat. Phys., 40, 725-750.

[48] Grassberger, P. [1985], "Generalizations of the Hausdorff dimension of fractal measures", Phys. Lett. A, 107, 101-105.

[49] Holzfuss, J., G. Mayer-Kress [1986], "An approach to error-estimation in the application of dimension algorithms", in [50], 114-122.

[50] Mayer-Kress, G. (ed.) [1986], Dimensions and Entropies in Chaotic Systems -Quantification of Complex Behavior, Berlin, Springer.

[51] Theiler, J. [1990], "Estimating fractal dimension", J. Opt. Soc. Am. A,7,1055-1073.

[52] Broggi, G. [1988], "Evaluation of dimensions and entropies of chaotic systems", J. Opt. Soc. Am. B, 5, 1020-1028.

[53] Oseledec, V.I. [1968], "A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems", Trans. Moscow Math. Soc., 19, 197-231.

[54] Benettin, G., L. Galgani, A. Giorgilli, J.-M. Strelcyn [1980], "Lyapunov characteristic exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part II: Numerical application " Meccanica, 15, 21-30. 16

[55] Shimada, I., T. Nagashima [1979], "A numerical approach to ergodic problems of dissipative dynamical systems", Prog. Theor. Phys., 61, 1605-1616.

[56] Eckmann, J.-P., D. Ruelle [1985], "Ergodic theory of chaos and strange attractors", Rev. Mod. Phys., 57, 617-656.

[57] Geist, K., U. Parlitz, W. Lauterborn [1990], "Comparison of Different Methods for Computing Lyapunov Exponents", Prog. Theor. Phys., 83, 875-893.

[58] Wolf, A., J.B. Swift, L. Swinney, J.A. Vastano [1985], "Determining Lyapunov exponents from a time series", Physica D, 16, 285-317.

[59] Sano, M.,Y. Sawada [1985], "Measurement of the Lyapunov spectrum from a chaotic time series", Phys. Rev. Lett., 55,1082-1085.

[60] Eckmann, J.-P., S.O. Kamphorst, D. Ruelle, S. Ciliberto [1986], "Lyapunov exponents from time series", Phys. Rev. A, 34, 4971-4979.

[61] Stoop, R.,P.F. Meier [1988], "Evaluation of Lyapunov exponents and scaling functions from time series", J. Opt. Soc. Am. B, 5, 1037-1045.

[62] Holzfuss, J.,W. Lauterborn [1989], "Liapunov exponents from a time series of acoustic chaos", Phys. Rev. A, 39, 2146-2152.

[63] Stoop, R.J. Parisi [1991], "Calculation of Lyapunov exponents avoiding spurious elements", Physica D, 50, 89-94.

[64] Zeng, X., R. Eykholt, R.A. Pielke [1991], "Estimating the Lyapunov-exponent spectrum from short time series of low precision", Phys. Rev. Lett., 66, 3229-3232.

[65] Zeng, X., R.A. Pielke, R. Eykholt [1992], "Extracting Lyapunov exponents from short time series of low precision", Modern Phys. Lett. B, 6, 55-75.

[66] Parlitz, U. [1993], "Lyapunov exponents from Chua's circuit", J. Circuits, Systems and Computers, 3, 507-523.

[67] Kruel, Th.M., M. Eiswirth, F.W. Schneider [1993], "Computation of Lyapunov spectra: Effect of interactive noise and application to a chemical oscillator", Physica D, 63, 117-137.

[68] Briggs, K. [1990], "An improved method for estimating Liapunov exponents of chaotic time series", Phys. Lett. A, 151, 27-32.

[69] Bryant, P., R. Brown, H.D.I. Abarbanel [1990], "Lyapunov exponents from observed time series", Phys. Rev. Lett., 65,1523-1526.

[70] Brown, R., P. Bryant, H.D.I. Abarbanel [1991], "Computing the Lyapunov spectrum of a dynamical system from an observed time series", Phys. Rev. A, 43, 2787-2806.

[71] Abarbanel, H.D.I., R. Brown, M.B. Kennel [1991], "Lyapunov exponents in chaotic systems: their importance and their evaluation using observed data", Int. J. Mod. Phys. B, 5, 1347-1375.

[72] Holzfuss, J, U. Parlitz [1991], "Lyapunov exponents from time series", Proceedings of the Conference Lyapunov Exponents, Oberwolfach 1990, eds. L. Arnold, H. Crauel, J.-P. Eckmann, in: Lecture Notes in Mathematics, Springer Verlag.

[73] Parlitz, U. [1992], "Identification of true and spurios Lyapunov exponents from time series", Int. J. Bifurcation and Chaos, 2, 155-165. 17

[74] Kadtke, J.B., J. Brush, J. Holzfuss [1993], "Global dynamical equations and Lyapunov exponents from noisy chaotic time series", Int. J. Bifurcation Chaos, 3, 607-616.

[75] Gencay, R., W.D. Dechert [1992], "An algorithm for the n Lyapunov exponents of an n-dimensional unknown dynamical system", Physica D, 59, 142-157.

[76] Eckmann, J.-P., D. Ruelle [1992], "Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems", Physical), 56, 185-187.

[77] Ellner, S., A.R. Gallant, D. McCaffrey, D. Nychka [1991], "Convergence rates and data requirements for Jacobian-based estimates of Lyapunov exponents from data", Phys. Lett. A, 153,357-363.

[78] Fell, J., J. Roschke, P. Beckmann [1993], "Deterministic chaos and the first positive Lyapunov exponent: a nonlinear analysis of the human electroencephalogram during sleep", Biol. Cybern., 69, 139-146.

[79] Fell, J., P. Beckmann [1994], "Resonance-like phenomena in Lyapunov calculations from data reconstructed by the time-delay method" Phys. Lett. A, 190, 172-176.

[80] Sato, S., M. Sano, Y. Sawada [1987], "Practical methods of measuring the generalized dimension and largest Lyapunov exponent in high dimensional chaotic systems", Prog. Theor. Phys., 77, 1-5.

[81] Kurths, J., H. Herzel [1987], "An attractor in solar time series", Physica D, 25,165-172.

[82] Dammig, M., F. Mitschke [1993], "Estimation of Lyapunov exponents from time series: the stochastic case", Phys. Lett. A, 178, 385-394.

[83] Rosenstein, M.T., J.J. Collins, C.J. de Luca [1993], "A practical method for calculating largest Lyapunov exponents from small data sets", Physica D, 65,117.

[84] Kantz, H. [1994], "A robust method to estimate the maximal Lyapunov exponent of a time series", Phys. Lett. A, 185, 77-87.

[85] Broomhead, D.S., J.P. Huke, M.R. Muldoon [1992], "Linear filters and nonlinear systems", /. Roy. Stat. Soc., B54, 373-382.

[86] Grassberger, P., R. Hegger, H. Kantz, C. Schaffrath, T. Schreiber [1993], "On noise reduction methods for chaotic data" CHAOS, 3,127-141.

[87] Kantz, H., T. Schreiber, I. Hoffmann, T. Buzug, G. Pfister, C.G. Flepp, J. Simonet, R. Badii, E. Brun [1993], "Nonlinear noise reduction: A case study on experimental data", Phys. Rev. E, 48,1529-1538.

[88] Kostelich, E.J.,T. Schreiber [1993], "Noise reduction in chaotic time-series data: A survey of common methods", Phys. Rev. E, 48, 1752-1763.

[89] Theiler, J., B. Galdrikian, A. Longtin, S. Eubank, J.D. Farmer [1992], "Using surrogate data to detect nonlinearity in time series" in: Nonlinear Modeling and Forecasting, eds. M. Casdagli and S. Eubank, SFI Studies in the Sciences of Complexity, Vol.XII (Reading, MA,Addison-Wesley) 163-188.

[90] Theiler, J., S. Eubank, A. Longtin, B. Galdrikian, J.D. Farmer [1992], "Testing for nonlinearity in time series: the method of surrogate data", Physica D, 58, 77-94. 18

[91] Provenzale, A., L.A. Smith, R. Vio, G. Murante [1992], "Distiguishing between lowdimensional dynamics and randomness in measured time series", Physica D, 58, 31-49.

[92] Smith, L. [1992], "Identification and prediction of low dimensional dynamics", Physica D, 58, 50-76.

[93] Takens, F. [1993], "Detecting nonlinearities in stationary time series", Int. J. of Bifurcation and Chaos, 3, 241-256.

[94] Wayland, R., D. Bromley, D. Pickett, A. Passamante [1993], "Recognizing determinism in a time series", Phys. Rev. Lett., 70, 580-582.

[95] Palus, M., V. Albrecht,I. Dvorak [1993], "Information theoretic test for nonlinearity in time series", Phys. lett. A, 175, 203-209.

[96] Kaplan, D. [1994], "Exceptional events as evidence for determinism", Physica D, 73, 38-48.

[97] Salvino, L.W., R. Cawley [1994], "Smoothness implies determinism: a method to detect it in time series", Phys. Rev. Lett., 73, 1091-1094.

[98] Savit, R.M. Green [1991], "Time series and dependent variables", Physica D, 50, 95-116.

[99] Rapp, P.E., A.M. Albano, I.D. Zimmerman, M.A. Jimenez-Moltano [1994], "Phaserandomized surrogates can produce spurious identifications of non-random structure", Phys. Lett. A, 192, 27-33.

[100] Fujisaka, H,,T. Yamada [1993], "Stability theory of synchronized motion in coupled oscillator systems," Prog. Theor. Phys., 69, 32-46.

[101] Singer, W. [1993], "Synchronization of cortical activity and its putative role in information processing and learning," Annu. Rev. Physiol., 55, 349-374.

[102] Ashwin, P., J. Buescu, I. Stewart [1994], "Bubbling of attractors and synchronisation of chaotic oscillators," Phys. lett. A, 193,126-139.

[103] Heagy, J.F., T.L. Carroll, L.M. Pecora [1994], "Synchronous chaos in coupled oscillator systems," Phys. Rev. E, 50, 1874-1885.

[104] Lai, Y.-C., C. Grebogi [1994], "Synchronization of spatiotemporal chaotic systems by feedback control," Phys. Rev. E, 50,1894-1899.

[105] Collins, J.J.,1. Stewart [1994], "A group-theoretic approach to rings of coupled biological oscillators," Biol. Cybern., 71, 95-103.

[106] Lindner, J.F., B.K. Meadows, W.L. Ditto, M.E. Inchiosa, A.R. Bulsara [1995], "Array enhanced stochastic resonance and spatiotemporal synchronization," Phys. Rev. Lett., 75, 3-6.

[107] Braiman, Y., W.L. Ditto, K. Wiesenfeld, M.L. Spano [1995], "Disorder-enhanced synchronization," Phys. Lett. A 206, 54-60; Braiman, Y., J.F. Lindner, W.L. Ditto [1995], "Taming spatiotemporal chaos with disorder," Nature, 378,465-467.

[108] Pecora, L.M., T.L. Carroll [1990], "Synchronization in chaotic systems," Phys. Rev. Lett., 64, 821-824; Carroll, T.L., L.M. Pecora [1991], IEEE Trans. Circuits Syst. 38, 453-456; Carroll T.L., L.M.Pecora [1992], Int. J. Bif. Chaos, 2, 659-667; Carroll, T.L., L.M.Pecora [1993], Physica D 67, 126-140; Carroll, T.L. [1994], Phys. Rev. E, 50, 25802587. 19

[109] Rulkov, N.F., K.M. Sushchik, L.S. Tsimring, H.D.I. Abarbanel, [1995], "Generalized synchronization of chaos in directionally coupled chaotic systems," Phys. Rev. E, 51, 980-995.

[110] Brown, R., N.F. Rulkov, E.R. Tracy [1994], «Modelling and synchronizing chaotic systems from experimental data," Phys. Lett. A, 194, 71-76.

[111] U. Parlitz, U. [1996], "Estimating model parameters from time series by autosynchronization," Phys. Rev. Lett., 76, 1232-1235

[112] Cuomo, K.M., A.V. Oppenheim [1993], "Circuit implementation of synchronized chaos with applications to communications," Phys. Rev. Lett., 71, 65-68; Oppenheim, A.V. G.W.Wornell, S.H.Isabelle, K.M. Cuomo [1992], "Signal processing in the context of chaotic signals," ProcIEEE ICASSP, IV 117-120.

[113] Kocarev, L., K.S. Halle, K. Eckert, L.O. Chua, U. Parlitz [1992], "Experimental demonstration of secure communications via chaotic synchronization," Int. J. Bifurcation and Chaos, 2, 709-713.

[114] Parlitz, U., L.O. Chua, L. Kocarev, K.S. Halle, A. Shang [1992], "Transmission of digital signals by chaotic synchronization," Int. J. Bifurcation and Chaos, 2, 973-977.

[115] Wu, C.W., L.O. Chua [1993], "A simple way to synchronize chaotic systems with applications to secure communication systems," Int. J. of Bifurcation and Chaos, 3, 1619-1627; Wu, C.W., L.O. Chua [1994], "A unified framework for synchronization and control of dynamical systems," Int. J. Bifurcation and Chaos, 4, 979-998.

[116] Halle, K.S., C.W. Wu, M. Itoh, L.O. Chua [1993], "Spread spectrum communication through modulation of chaos," Int. J. Bifurcation and Chaos, 3, 469-477.

[117] Kocarev, L., U. Parlitz [1995], "General approach for chaotic synchronization with applications to communcation," Phys. Rev. Lett., 74, 5028-5031; "Communication using chaotic signals," in: Proceedings of Nonlinear Dynamics of Electronic Systems, Krakow, Poland, 29 - 30 July, 1994.

[118] Parlitz, U., L. Kocarev, T. Stojanovski, H. Preckel [1996], "Encoding messages using chaotic synchronization," to appear in: Phys. Rev. E.

[119] Parlitz, U. L. Kocarev [1996], "Multichannel communication using auto-synchronization," to appear in: Int. J. Bifurcation and Chaos.

[120] Short, K.M. [1994], "Steps toward unmasking secure communications," Int. J. Bifurcation and Chaos, 4, 959-977.

[121] Pérez, G., H.A. Cerdeira [1995], "Extracting messages masked by chaos," Phys. Rev. Lett., 74,1970-1973.

[122] Lorenz, E.N. [1963], "Deterministic nonperiodic flow",/. Atmos. Sci., 20,130-141.

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