Stochastic stability analysis of a reduced galactic dynamo model with perturbed -effect

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• 作者：Có ; nall Kelly ^{conall.kelly@uwimona.edu.jm" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Stochastic differential equations ; Lyapunov exponents ; Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
• 刊名：Physica A: Statistical Mechanics and its Applications
• 出版年：2016
• 出版时间：1 September 2016
• 年：2016
• 卷：457
• 期：Complete
• 页码：480-491
• 全文大小：607 K

文摘

We investigate the asymptotic behaviour of a reduced user=111111111&_pii=S0378437116301066&_rdoc=1&_issn=03784371&md5=18b846c5b5e0672e9fe25e9b173c28ad" title="Click to view the MathML source">αΩ$\alpha \Omega$-dynamo model of magnetic field generation in spiral galaxies where fluctuation in the user=111111111&_pii=S0378437116301066&_rdoc=1&_issn=03784371&md5=45c742e66a71ea463b6f671611e27a91" title="Click to view the MathML source">α$\alpha$-effect results in a system with state-dependent stochastic perturbations.

By computing the upper Lyapunov exponent of the linearised model, we can identify regions of instability and stability in probability for the equilibrium of the nonlinear model; in this case the equilibrium solution corresponds to a magnetic field that has undergone catastrophic quenching. These regions are compared to regions of exponential mean-square stability and regions of sub- and super-criticality in the unperturbed linearised model. Prior analysis in the literature which focuses on these latter regions does not adequately address the corresponding transition in the nonlinear stochastic model.

Finally we provide a visual representation of the influence of drift non-normality and perturbation intensity on these regions.