On the trajectory method for the reconstruction of differential equations from time series

Nonlinear Dynamics

Volumn 23, Issue 1, 2000, Pages 13-33

  Perona, Paolo ^a   Porporato, Amilcare ^a   Ridoefi, Euca ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

LINEAR EQUATIONS; OSCILLATORS (MECHANICAL); SPURIOUS SIGNAL NOISE; TIME SERIES ANALYSIS;

SAMPLING FREQUENCY; TRAJECTORY METHODS; VAN DER POL MODELS;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 0034276175     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008335507636     Document Type: Article

References (23)

1. Eisenhammer, T., Hübler, A., Packard, N., and Kelso, J. A. S., 'Modeling experimental time series with ordinary differential equations', Biological Cybernetics 65, 1991, 107-112.
2. Billings, S. A., 'Identification of nonlinear systems - A survey', Institute of Electrical and Electronics Engineering Proceedings 127D, 1980, 272-285.
3. Judd, K. and Mees, A., 'On selecting models for nonlinear time series', Physica D 82, 1995, 426-444.
4. Abarbanel, H. D. J., Brown, R., Sidorovich, J. J., and Tsimring, L. S., 'The analysis of observed chaotic data in physical systems', Review of Modern Physics 65(4), 1993, 1331-1392.
5. Crutchfield, J. P. and McNamara, B. S., 'Equations of motion from a data series', Complex Systems 1, 1986, 417-452.
6. Cremers, J. and Hübler, A., 'Construction of differential equations from experimental data', Zeitschrift für Naturforschung A 42, 1986, 797-802.
7. Breeden, J. L. and Hübler, A., 'Reconstructing equation of motion from experimental data with unobserved variables', Physical Review A 42(10), 1990, 5817-5826.
8. Baake, E., Baake, M., Bock, H. G., and Briggs, K. M., 'Fitting ordinary differential equations to chaotic data', Physical Review A 45(8), 1992, 5524-5529.
9. Rowlands, G. and Sprott, J. C., 'Extraction of dynamical equations from chaotic data', Physica D 58, 1992, 251.
10. Gouesbet, G. and Maquet, J., 'Construction of phenomenological models from numerical scalar time series', Physica D 58, 1992, 202-215.
11. He, X. and Lapedes, A., 'Nonlinear modeling and prediction by successive approximation using radial basis functions', Physica D 70, 1993, 289-301.
12. Aguirre, L. A. and Billings, S. A., 'Identification of models for chaotic systems from noisy data: Implications for performance and nonlinear filtering', Physica D 85, 1995, 239-258.
13. Yannacopoulos, A. N., Brindley, J., Merkin, J. H., and Pilling, M. J., 'Approximation of attractors using Chebyshev polynomials', Physica D 99, 1996, 162-174.
14. Aguirre, L. A., 'Recovering map static nonlinearities from chaotic data using dynamical models', Physica D 100, 1997, 41-57.
15. Borland, L., 'Simultaneous modeling of nonlinear deterministic and stochastic dynamics', Physica D 99, 1996, 175-190.
16. Irving, A. D. and Dewson, T., 'Determining mixed linear-nonlinear coupled differential equations from multivariate discrete time series sequences', Physica D 102, 1997, 15-36.
17. Ohle, F., Eckelmann, H., and Hübler, A., 'Description of transient states of von Karman vortex streets by low-dimensional differential equations', Physics of Fluids A 2(4), 1990, 479-481.
18. Ohle, R and Eckelmann, H., 'Modeling of a von Karman vortex street at low Reynolds numbers', Physics of Fluids A 4(8), 1992, 1707-1714.
19. Judd, K. and Mees, A., 'Modeling chaotic motions of string from experimental data', Physica D 92, 1996, 221-236.
20. Casdagli, M., Eubank, S., Farmer, J. D., and Gibson, J., 'State space reconstruction in the presence of noise', Physica D 51, 1991, 52-71.
21. Porporato, A. and Ridolfi, L., 'Nonlinear analysis of near-wall turbulent time series', Applied Scientific Research 57, 1997, 235-261.
22. Perona, P., Porporato, A., and Ridolfi, L., 'A simple experimental equation for the bursting cycle', Physics of Fluids 10(11), 1998, 3023-3026.
23. Saltzman, B., 'Climatic system analysis', Advances in Geophysics 25, 1983, 173-233.