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

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  • I. Lubashevsky
  • M. Hajimahmoodzadeh
  • A. Katsnelson
  • P. Wagner

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. Copyright Springer-Verlag Berlin/Heidelberg 2003

Suggested Citation

  • I. Lubashevsky & M. Hajimahmoodzadeh & A. Katsnelson & P. Wagner, 2003. "Noised-induced phase transition in an oscillatory system with dynamical traps," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 36(1), pages 115-118, November.
    • Handle: RePEc:spr:eurphb:v:36:y:2003:i:1:p:115-118
    DOI: 10.1140/epjb/e2003-00323-0
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    References listed on IDEAS

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    1. Eckhard Platen, 1999. "An Introduction to Numerical Methods for Stochastic Differential Equations," Research Paper Series 6, Quantitative Finance Research Centre, University of Technology, Sydney.
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