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Noised-induced phase transition in an oscillatory system with dynamical traps

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Abstract.

A new type of noised induced phase transitions is proposed. It occurs in noisy systems with dynamical traps. Dynamical traps are regions in the phase space where the regular “forces” are depressed substantially. By way of an example, a simple oscillatory system \(\{x,v = \dot{x}\}\) with additive white noise is considered and its dynamics is analyzed numerically. The dynamical trap region is assumed to be located near the x-axis where the “velocity” v of the system becomes sufficiently low. The meaning of this assumption is discussed. The observed phase transition is caused by the asymmetry in the residence time distribution in the vicinity of zero value “velocity”. This asymmetry is due to a cooperative effect of the random Langevin “force” in the trap region and the regular “force” not changing the direction of action when crossing the trap region.

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Authors and Affiliations

  1. Theory Department, General Physics Institute, Russian Academy of Sciences, Vavilov Str. 38, 119991, Moscow, Russia

    I. Lubashevsky

  2. Faculty of Physics, M.V. Lomonosov Moscow State University, 119992, Moscow, Russia

    M. Hajimahmoodzadeh & A. Katsnelson

  3. Institute of Transport Research, German Aerospace Center (DLR), Rutherfordstrasse 2, 12489, Berlin, Germany

    P. Wagner

Authors
  1. I. Lubashevsky
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  2. M. Hajimahmoodzadeh
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  3. A. Katsnelson
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  4. P. Wagner
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Corresponding author

Correspondence to I. Lubashevsky.

Additional information

Received: 25 April 2003, Published online: 19 November 2003

PACS:

05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 05.45.-a Nonlinear dynamics and nonlinear dynamical systems - 05.70.Fh Phase transitions: general studies

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Lubashevsky, I., Hajimahmoodzadeh, M., Katsnelson, A. et al. Noised-induced phase transition in an oscillatory system with dynamical traps. Eur. Phys. J. B 36, 115–118 (2003). https://doi.org/10.1140/epjb/e2003-00323-0

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  • DOI: https://doi.org/10.1140/epjb/e2003-00323-0

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