Estimation of parameters in one-dimensional maps from noisy chaotic time series

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 336, Issue 6, 2005, Pages 448-458

  Smirnov, Dmitry A ^a   Vlaskin, Vladislav S ^b   Ponomarenko, Vladimir I ^a,b  

^a INSTITUTE OF RADIO ENGINEERING AND ELECTRONICS   (Russian Federation)

^b SARATOV STATE UNIVERSITY   (Russian Federation)

Author keywords

Deterministic chaos; Modelling from time series; One dimensional maps; Parameter estimation; Time series analysis

Indexed keywords

COST BENEFIT ANALYSIS; COST FUNCTIONS; GLOBAL OPTIMIZATION; MAXIMUM LIKELIHOOD ESTIMATION; TIME SERIES ANALYSIS;

BACKWARD ITERATIONS; CHAOTIC TIME SERIES; DETERMINISTIC CHAOS; ESTIMATION OF PARAMETERS; GLOBAL OPTIMISATION; MAXIMUM LIKELIHOOD PRINCIPLES; NUMERICAL EXPERIMENTS; ONE DIMENSIONAL MAP;

PARAMETER ESTIMATION;

ARTICLE; COST; MATHEMATICAL MODEL; MAXIMUM LIKELIHOOD METHOD; MODEL; NOISE; PARAMETER; TECHNIQUE; THEORETICAL MODEL;

EID: 14144251956     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physleta.2004.12.092     Document Type: Article

References (27)

1. R. Hegger, H. Kantz, and F. Schmuser Chaos 8 1998 727
2. I. Swameye, T.G. Muller, and J. Timmer Proc. Natl. Acad. Sci. USA 100 2003 1028
3. L. Ljung System Identification. Theory for the User 1991 Moscow
4. H. Kantz, and T. Schreiber Nonlinear Time Series Analysis 1997 Cambridge Univ. Press Cambridge
5. G. Gouesbet S. Meunier-Guttin-Cluzel O. Menard Chaos and its Reconstructions 2003 Nova Science Publishers New York
6. E. Baake, M. Baake, H.J. Bock, and K.M. Briggs Phys. Rev. A 45 1992 5524
7. R. Brown, N.F. Rulkov, and E.R. Tracy Phys. Lett. A 194 1994 71
8. V.S. Anishchenko, A.N. Pavlov, and N.B. Janson Chaos Solitons Fractals 8 1998 1267
9. J. Timmer, H. Rust, W. Horbelt, and H.U. Voss Phys. Lett. A 274 2000 123
10. B.P. Bezruchko, and D.A. Smirnov Phys. Rev. E 63 2001 016207
11. A. Sitz, U. Schwartz, J. Kurths, and H.U. Voss Phys. Rev. E 66 2002 016210
12. M. Casdagli Physica D 35 1989 335
13. L.A. Smith Physica D 58 1992 50
14. K. Judd, and A.I. Mees Physica D 82 1995 426
15. L.A. Aguirre, and E.M.A.M. Mendes Int. J. Bifur. Chaos 6 1996 279
16. U. Parlitz, and C. Merkwirth Phys. Rev. Lett. 84 2000 1890
17. A.M. Feigin, Ya.I. Mol'kov, D.N. Mukhin, and Ye.M. Loskutov Izv. Vyssh. Uchebn. Zaved. Radiofiz. 44 5-6 2001 376
18. D. Smirnov, and B. Bezruchko Phys. Rev. E 68 2003 046209
19. G. Gouesbet S. Meunier-Guttin-Cluzel O. Ménard Chaos and its Reconstruction 2003 Cambridge Univ. Press Cambridge 1 160
20. L. Jaeger, and H. Kantz Chaos 6 1996 440
21. P.E. McSharry, and L.A. Smith Phys. Rev. Lett. 83 1999 4285
22. K. Judd Phys. Rev. E 67 2003 026212
23. W. Horbelt, and J. Timmer Phys. Lett. A 310 2003 269
24. V.F. Pisarenko, and D. Sornette Phys. Rev. E 69 2004 036122
25. J.D. Farmer, and J.J. Sidorowich Physica D 47 1991 373
26. Yu.V. Andreyev, A.S. Dmitriev, and E.V. Efremova Phys. Rev. E 65 2002 046220
27. J.E. Dennis, and R.B. Schnabel Numerical Methods for Unconstrained Optimization and Nonlinear Equations 1983 Prentice-Hall Englewood Cliffs, NJ