Abstract
The Rössler system is used as an example to demonstrate that the reconstruction of a model nonlinear dynamical system from an observed time series reveals phase-space regions called channels and jokers [3]. The proposed method for finding such regions is shown to be robust to noise and inaccuracy (redundancy) of the models used in the reconstruction procedure. The evolution of local Lyapunov exponents of attractors is examined for the model systems, and its relation to channels and jokers is exposed. It is shown that channels and jokers can be used in predictive modeling. The quality of such models is analyzed by invoking the concept of degree of predictability.
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References
Yu. A. Kravtsov, Usp. Fiz. Nauk 158, 93 (1989) [Sov. Phys. Usp. 32, 434 (1989)].
H. G. Schuster, Deterministic Chaos (Physik, Weinheim, 1984; Mir, Moscow, 1988).
G. G. Malinetskiĭ and A. B. Potapov, Preprint No. 32, IPM RAN (Keldysh Inst. of Applied Mathematics, Russian Academy of Sciences, Moscow, 1998).
I. Bellachook and G. Malinetskii, in Proceedings of 5th International Specialist Workshop on Nonlinear Dynamics of Electronic Systems (Moscow, 1997), p. 40.
S. P. Kuznetsov, Dynamical Chaos (Fizmatlit, Moscow, 2001) [in Russian].
O. L. Anosov, O. Ya. Butkovskiĭ, and Yu. A. Kravtsov, Radiotekh. Élektron. (Moscow) 42(3), 1 (1997) [J. Commun. Technol. Electron. 42, 288 (1997)].
B. P. Bezruchko and D. A. Smirnov, Creation of Model Representations on the Basis of Chaotic Time Series (GosUNTs “Kolledzh”, Saratov, 2000) [in Russian].
O. Ya. Butkovskiĭ and Yu. A. Kravtsov, in Proceedings of Seminar on Time, Chaos, and Mathematical Problems (Knizhnyĭ Dom “Universitet,” Moscow, 1999), No. 1, p. 165.
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Original Russian Text © O.Ya. Butkovskiĭ, M. Yu. Logunov, 2007, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 131, No. 6, pp. 1107–1114.