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Stochastic analysis of subcritical amplification of magnetic energy in a turbulent dynamo

Author

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  • Fedotov, Sergei
  • Bashkirtseva, Irina
  • Ryashko, Lev

Abstract

We present and analyze a simplified stochastic αΩ-dynamo model which is designed to assess the influence of additive and multiplicative noises, non-normality of dynamo equation, and nonlinearity of the α-effect and turbulent diffusivity, on the generation of a large-scale magnetic field in the subcritical case. Our model incorporates random fluctuations in the α-parameter and additive noise arising from the small-scale fluctuations of magnetic and turbulent velocity fields. We show that the noise effects along with non-normality can lead to the stochastic amplification of the magnetic field even in the subcritical case. The criteria for the stochastic instability during the early kinematic stage are established and the critical value for the intensity of multiplicative noise due to α-fluctuations is found. We obtain numerical solutions of nonlinear stochastic differential equations and find the series of phase transitions induced by random fluctuations in the α-parameter.

Suggested Citation

  • Fedotov, Sergei & Bashkirtseva, Irina & Ryashko, Lev, 2004. "Stochastic analysis of subcritical amplification of magnetic energy in a turbulent dynamo," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(3), pages 491-506.
    • Handle: RePEc:eee:phsmap:v:342:y:2004:i:3:p:491-506
    DOI: 10.1016/j.physa.2004.05.084
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    Citations

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    Cited by:

    1. Kelly, Cónall, 2016. "Stochastic stability analysis of a reduced galactic dynamo model with perturbed α-effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 480-491.
    2. Ryashko, L. & Bashkirtseva, I. & Gubkin, A. & Stikhin, P., 2009. "Confidence tori in the analysis of stochastic 3D-cycles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 256-269.
    3. Bashkirtseva, Irina & Ryashko, Lev, 2005. "Sensitivity and chaos control for the forced nonlinear oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1437-1451.

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