Abstract
The problem of transition of a noisy dynamical system to a periodic oscillatory regime through a zone of chaos is considered. Using the noisy logistics map as an example, domains of attraction of energetically equivalent regimes of period three are found for various transition rates and various noise levels. The fine structure of the domains of attraction under the condition of fast transitions is revealed. It is discovered that the settling time of the stable cycle of period three heavily depends on the initial conditions, i.e., on the structure of the domains of attraction. The critical transition rate that separates the region of the probabilistic symmetry of final states from the region of the dynamic behavior of trajectories is estimated.
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Translated from Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 122, No. 1, 2002, pp. 198–204.
Original Russian Text Copyright © 2002 by Bilchinskaya, Butkovski\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \), Kravtsov, Rychka, Surovyatkina.
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Bilchinskaya, S.G., Butkovskii, O.Y., Kravtsov, Y.A. et al. The probabilistic symmetry breaking of periodic regimes rapidly passing through a zone of chaos into the transparency window. J. Exp. Theor. Phys. 95, 175–180 (2002). https://doi.org/10.1134/1.1499915
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DOI: https://doi.org/10.1134/1.1499915