Improved cost functions for modelling of noisy chaotic time series

Physica D: Nonlinear Phenomena

Volumn 109, Issue 1-2, 1997, Pages 59-69

  Kantz, Holger ^a   Jaeger, Lars ^a  

^a MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

Author keywords

Modelling; Noise; Time series analysis

Indexed keywords

EID: 0001986872     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(97)00159-0     Document Type: Article

References (22)

1. N.H. Packard, J.P. Crutchfield, J.D. Farmer and R.S. Shaw, Geometry from a time series, Phys. Rev. Lett. 45 (1980) 712-716.
2. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis, Nonlinear Science Series No. 7 (Cambridge University Press, Cambridge, 1997).
3. H. Kantz and T. Schreiber, Dimension estimates and physiological data, Chaos 5 (1995) 143.
4. J. Palis and F. Takens, Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge Studies in Advanced Mathematics (Cambridge University Press, Cambridge, 1993).
5. M. Viana, personal communication.
6. J.-P. Eckmann, S. Oliffson Kamphorst, D. Ruelle and S. Ciliberto, Liapunov exponents from time series, Phys. Rev. A 34 (1986) 4971-4979.
7. D.S. Broomhead and D. Lowe, Multivariate functional interpolation and adaptive networks, Complex systems 2 (1988) 321-355.
8. M. Casdagli, Chaos and deterministic versus stochastic nonlinear modelling, J. Roy. Stat. Soc. B 54 (1991) 303.
9. R. Gencay and W.D. Dechert, An algorithm for the n Lyapunov exponents of an n-dimensional unknown dynamical system, Physica D 59 (1992) 142-157.
10. F. Takens, Detecting Strange Attractors in Turbulence, Lecture Notes in Mathematics, Vol. 898 (Springer, New York, 1981);
11. T. Sauer, J. Yorke and M. Casdagli, Embedology, J. Stat. Phys. 65 (1991) 579.
12. A.G. Darbyshire and D.S. Broomhead, Robust estimation of tangent maps and Lyapunov spectra, Physica D 89 (1996) 287.
13. L. Jaeger and H. Kantz, Unbiased reconstruction of the dynamics underlying noisy chaotic data, Chaos 6 (1996) 440.
14. R. Hegger, L. Jaeger and H. Kantz, Efficient reconstruction of the dynamics of multivariate time series, preprint MPIPKS.
15. H. Kantz, T. Schreiber, I. Hoffmann, T. Buzug, G. Pfister, L.G. Flepp, J. Simonet, R. Badii and E. Brun, Nonlinear noise reduction: A case study on experimental data, Phys. Rev. E 48 (1993) 1529.
16. F.T. Arecchi, W. Gadomski and R. Meucci, Generation of chaotic dynamics by feedback on a laser, Phys. Rev. A 34 (1985) 1617;
17. M. Ciofini, R. Meucci and F.T. Arecchi, Experimental control of chaos in a laser, Phys. Rev. E 52 (1995) 94.
18. B.V. Anosov, Proc. Steklov Inst. Math. 90 (1) (1967);
19. R. Bowen, J. Differential Equations 18 (1975) 333.
20. H.E. Nusse and J.A. Yorke, Comm. Math. Phys. 114 (1988) 363-379.
21. L. Jaeger and H. Kantz, Homoclinic tangencies and non-normal Jacobians - effects of noise in non-hyperbolic chaotic systems, Physica D 105 (1997) 79-96.
22. L. Jaeger and H. Kantz, Effective deterministic models for chaotic motion perturbed by interactive noise, Phys. Rev. E 55 (1997) 5234.