Abstract
In the paper a new three-dimensional visualization technique of results of methods of prediction of chaotic time series has been analyzed. The influence of graphical presentation of attractors on the quality of forecasting results has been tested. The following methods of prediction of behaviours of chaotic dynamical systems have been considered: method of analogs, centre-of-mass-prediction method and local linear prediction method. The forecasting quality has been evaluated with using the error function and the correlation coefficient. It has been shown that 3D visualization of attractor is a necessary condition for obtaining the proper result of forecasting with using the deterministic chaos methods.
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6 References
Box G. E. P., Jenkis G. M., „Analiza szeregów czasowych i prognozowanie, Wydawnictwo Naukowe PWN, Warszawa 1983.
Schuster H.G., Chaos deterministyczny — wprowadzenie, Wydawnictwo Naukowe PWN, Warszawa 1993.
Mosdorf R., Shoji M., Chaos in bubbling — nonlinear analysis and modeling, Chemical Engineering Science 58, 3837–3846, 2003.
Singh S., Multiple forecasting using local approximation, Pattern Recognition, 34, 443–445, 2001.
Reick Ch. H., Page B., Time series prediction by multivariate next neighbor methods with application to zooplankton forecasts, Mathematics and Computers in simulation 52, 289–310, 2000.
Baker G.L., Gollub J.P., Wstęp do dynamiki układów chaotycznych, Wydawnictwo Naukowe PWN, Warszawa, 1998.
Abarbanel H. D. I., Brown R., Sidorowich J. J., Tsimring L. S., The analysis of observed chaotic data in physical system, Reviews of Modern Physics, 65(4), 1331–1392, October 1993.
Little S., Ellner S., Pascual M., Kaplan D., Sauer T., Caswell H., Solow A., Detecting nonlinear dynamics in spatio-temporal systems, examples from ecological models, Physica D 96, 321–333, 1996.
Sidorowich J.J., Farmer J.D., Predicting chaotic time series, Physical Review Letters, 59(8), 1987.
Żmijkowska M., Wykorzystanie analizy fraktalnej w prognozowaniu. Praca magisterska, Politechnika Białostocka, 2003.
Sidorowich J.J., Farmer J.D., Predicting chaotic time series, Physical Review Letters, 59(8), 845–848, 1987.
Hyrskykari A., Development of Program Visualization Systems, 2nd Czech British Symposium of Visual Aspects of Man-Machine, Systems, Praha, 1993.
Szmal P., Francik J., Nowak M., Systemy wizualizacji algorytmów wspomagające badania naukowe, III Konferencja Komputery w badaniach naukowych KOWBAN, 317–322, Polanica Zdrój, 1996.
Peters E.E., Teoria chaosu a rynki kapitałowe, WIG-Press, Warszawa 1997.
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Pankiewicz, M., Mosdorf, R. (2005). The prediction of behaviours of chaotic dynamical systems in 3D state space. In: Saeed, K., Pejaś, J. (eds) Information Processing and Security Systems. Springer, Boston, MA. https://doi.org/10.1007/0-387-26325-X_34
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DOI: https://doi.org/10.1007/0-387-26325-X_34
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-25091-5
Online ISBN: 978-0-387-26325-0
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