Abstract
A method for determining the transient process duration in a dynamical system with quasiperiodic behavior is described. An analytical expression is obtained that relates the average transient process duration to the accuracy of determination of this parameter.
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B. P. Bezruchko, T. V. Dikanev, and D. A. Smirnov, Izv. Vyssh. Uchebn. Zaved., Prikl. Neline\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \)naya Dinam. 9(3), 3 (2001).
B. P. Bezruchko, T. V. Dikanev, and D. A. Smirnov, Phys. Rev. E 64, 036210 (2001).
C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 50, 935 (1983).
L. Zhu, A. Raghu, and Y.-C. Lai, Phys. Rev. Lett. 86, 4017 (2001).
V. V. Astakhov et al., Radiotekh. Élektron. (Moscow) 38, 291 (1993).
É. V. Kal’yanov, Pis’ma Zh. Tekh. Fiz. 26(15), 26 (2000) [Tech. Phys. Lett. 26, 656 (2000)].
C. Grebogi, E. Ott, and J. A. Yorke, Physica D 7, 181 (1983).
H. E. Nusse and J. A. Yorke, Physica D 36, 137 (1989).
I. M. Janosi and T. Tél, Phys. Rev. E 49, 2756 (1994).
M. Dhamala, Y.-C. Lai, and E. J. Kostelich, Phys. Rev. E 64, 056207 (2001).
M. Dhamala, Y.-C. Lai, and E. J. Kostelich, Phys. Rev. E 61, 6485 (2000).
A. A. Koronovskii, I. S. Rempen, D. I. Trubetskov, and A. E. Khramov, Izv. Ross. Akad. Nauk, Ser. Fiz. 66, 1754 (2002).
A. A. Koronovskii, D. I. Trubetskov, A. E. Khramov, and A. E. Khramova, Dokl. Akad. Nauk 383, 322 (2002) [Dokl. Phys. 47, 181 (2002)].
A. A. Koronovskii, D. I. Trubetskov, A. E. Khramov, and A. E. Khramova, Izv. Vyssh. Uchebn. Zaved., Radiofiz. 45, 880 (2002).
A. A. Koronovskii and A. E. Khramov, Pis’ma Zh. Tekh. Fiz. 28(15), 61 (2002) [Tech. Phys. Lett. 28, 648 (2002)].
A. A. Koronovskii, A. E. Khramov, and I. A. Khramova, Izv. Vyssh. Uchebn. Zaved., Prikl. Neline\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \)naya Dinam. 11, 1 (2002).
M. Hénon, Physica D 5, 412 (1982).
Z. Kaufmann and H. Lustfeld, Phys. Rev. E 64, 055206 (2001).
H. G. Schuster, Deterministic Chaos (Physik-Verlag, Weinheim, 1984; Mir, Moscow, 1988).
G. P. Bystrai and S. I. Studentok, Izv. Vyssh. Uchebn. Zaved., Prikl. Nelineinaya Dinam. 10(6), 24 (2002).
A. A. Koronovskii, A. V. Starodubov, and A. E. Khramov, Izv. Vyssh. Uchebn. Zaved., Prikl. Neline\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \)naya Dinam. 10(5), 25 (2002).
A. A. Koronovskii, A. V. Starodubov, and A. E. Khramov, Pis’ma Zh. Tekh. Fiz. 29(8), 32 (2003) [Tech. Phys. Lett. 29, 323 (2003)].
G. M. Zaslavsky, Chaos in Dynamical Systems (Nauka, Moscow, 1984; Harwood, Chur, 1985).
G. M. Zaslavskii, Statistical Irreversibility in Nonlinear Systems (Nauka, Moscow, 1970).
R. Z. Sagdeev, D. A. Usikov, and G. M. Zaslavsky, Nonlinear Physics: from the Pendulum to Turbulence and Chaos (Harwood, Chur, 1988); Russian original: G. M. Zaslavsky and R. Z. Sagdeev, Introduction to Nonlinear Physics (Nauka, Moscow, 1988).
S. P. Kuznetsov, Dynamical Chaos (Fizmatlit, Moscow, 2001).
G. B. Astaf’ev, A. A. Koronovski\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\), A. E. Khramov, and A. E. Khramova, Izv. Vyssh. Uchebn. Zaved., Prikl. Neline\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \)naya Dinam. (2003, in press).
G. Benettin, L. Galgani, A. Giorgilli, and J.-M. Strelcyn, Meccanica 15, 9 (1980).
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Translated from Pis’ma v Zhurnal Tekhnichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 29, No. 19, 2003, pp. 31–39.
Original Russian Text Copyright © 2003 by Koronovski\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \).
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Koronovskii, A.A. Dependence of the transient process duration on the accuracy of determination in dynamical systems with quasiperiodic behavior. Tech. Phys. Lett. 29, 806–809 (2003). https://doi.org/10.1134/1.1623852
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DOI: https://doi.org/10.1134/1.1623852