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Stochastic Anti-Resonance in Polarization Phenomena

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The Foundations of Chaos Revisited: From Poincaré to Recent Advancements

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

The phenomenon of resonant stochastization, so-called stochastic anti-resonance, is considered on an example of Raman fibre amplifier with randomly varying birefringence. Despite a well-known effect of noise suppression and global regularization of dynamics due to resonant interaction of noise and regular external periodic perturbation, as it takes a place in the case of stochastic resonance, here we report about reverse situation when regular perturbation assists a noise-induced escape of a system from metastable state. Such an escape reveals itself by different signatures like growth of dispersion, dropping of Hurst parameter and Kramers length characterizing behavior of physically relevant parameters (e.g. average gain and projection of signal state of polarization to pump one). This phenomenon is analyzed by the means of two techniques: direct numerical simulations of underlying stochastic differential equations and multi-scale averaging method reducing a problem to a set of deterministic ordinary differential equations for average values characterizing the states of polarization. It is shown, that taking into account a relevant set of scales characterizing a system results in excellent agreement between results of direct numerical simulations and average model. It is very challenging outcome because allows replacing the cumbersome numerical simulations and revealing the system-relevant signatures for many important real-world systems.

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Acknowledgements

Support of the FP7-PEOPLE-2012-IAPP (project GRIFFON, No. 324391) is acknowledged. The computational results have been achieved using the Vienna Scientific Cluster (VSC).

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Authors and Affiliations

  1. Aston Institute of Photonic Technologies, Aston University, Birmingham, B4 7ET, UK

    Vladimir L. Kalashnikov & Sergey V. Sergeyev

Authors
  1. Vladimir L. Kalashnikov
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  2. Sergey V. Sergeyev
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Correspondence to Vladimir L. Kalashnikov .

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Editors and Affiliations

  1. ManLab Technical University of Crete, Chania, Greece

    Christos Skiadas

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Kalashnikov, V.L., Sergeyev, S.V. (2016). Stochastic Anti-Resonance in Polarization Phenomena. In: Skiadas, C. (eds) The Foundations of Chaos Revisited: From Poincaré to Recent Advancements. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-29701-9_10

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