Abstract
The transient chaos regime in a two-dimensional system with discrete time (Eno map) is considered. It is demonstrated that a time series corresponding to this regime differs from a chaotic series constructed for close values of the control parameters by the presence of “nonregular” regions, the number of which increases with the critical parameter. A possible mechanism of this effect is discussed.
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References
C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 48, 1507 (1982).
G. Ahlers and R. W. Walden, Phys. Rev. Lett. 44, 445 (1980).
L. Zhu, A. Raghu, and Y.-C. Lai, Phys. Rev. Lett. 86, 4017 (2001).
M. Dhamala and Y.-C. Lai, Phys. Rev. E 59, 1646 (1999).
H. W. Yin and J.-H. Dai, Phys. Rev. E 54, 371 (1996).
A. A. Koronovskii, I. S. Rempen, D. I. Trubetskov, and A. E. Khramov, Izv. Ross. Akad. Nauk, Ser. Fiz. 66, 1754 (2002).
M. Woltering and M. Markus, Phys. Rev. Lett. 84, 630 (2000).
M. Dhamala and Y.-C. Lai, Phys. Rev. E 60, 6176 (1999).
M. Dhamala, Y.-C. Lai, and E. J. Kostelich, Phys. Rev. E 61, 6485 (2000).
M. Dhamala, Y.-C. Lai, and E. J. Kostelich, Phys. Rev. E 64, 056207 (2001).
I. M. Janosi and T. Tel, Phys. Rev. E 49, 2756 (1994).
H. E. Nusse and J. A. Yorke, Physica D 36, 137 (1989).
P. D. S. Moresco, Physica D 126, 38 (1999).
D. Sweet, H. E. Nusse, and J. A. Yorke, Phys. Rev. Lett. 86, 2261 (2001).
M. Hénon, Commun. Math. Phys. 50, 69 (1976).
A. A. Koronovskii, A. V. Starodubov, and A. E. Khramov, Izv. Vyssh. Uchebn. Zaved. Prikl. Nelineinaya Din. 10(5), 25 (2002).
P. Manneville and Y. Pomeau, Physica D 1, 167 (1980).
H. G. Shuster, Deterministic Chaos (Physik-Verlag, Weinheim, 1984; Mir, Moscow, 1998).
C. Grebogi, E. Ott, F. Romeiras, and J. A. Yorke, Phys. Rev. A 36, 5365 (1987).
C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 57, 1284 (1986).
T. S. Parker and L. O. Chua, Practical Numerical Algorithms for Chaotic Systems (Springer-Verlag, Berlin, 1989).
Z. P. You, E. J. Kostelich, and J. A. Yorke, Int. J. Bifurcation Chaos Appl. Sci. Eng. 1, 605 (1991).
E. J. Kostelich, J. A. Yorke, and Z. Yuo, Physica D 93, 210 (1996).
C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 56, 1011 (1986).
H. E. Nusse, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 75, 2482 (1995).
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Translated from Pis’ma v Zhurnal Tekhnichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 29, No. 22, 2003, pp. 1–9.
Original Russian Text Copyright © 2003 by Astaf’ev, Koronovski\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \), Khramov.
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Astaf’ev, G.B., Koronovskii, A.A. & Khramov, A.E. Behavior of dynamical systems in the regime of transient chaos. Tech. Phys. Lett. 29, 923–926 (2003). https://doi.org/10.1134/1.1631365
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DOI: https://doi.org/10.1134/1.1631365