Geodesic
Stochastic two-mode hereditary model of a cosmic dynamo
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 48 (2024) no. 3, pp. 70-82

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The paper is devoted to a class of stochastic two-mode hereditary models of the cosmic dynamo. The models include two magnetic field generators — large-scale and turbulent ($\alpha$-effect). The influence of the magnetic field on the motion of the medium is presented through the suppression of the $\alpha$-effect by a functional of the field components, which introduces memory (hereditary) into the model. The model describes the dynamics of only large-scale components, but takes into account the possible impact of smallscale modes using a stochastic term. This term models the influence of possible spontaneous synchronization of small-scale modes. The paper also presents a numerical scheme for solving the integro-differential equations of the model. The numerical scheme consists of two parts, for the differential part the Adams «predictor-corrector» method of the fourth order is used, and for the integral part the Simpson method.The main result of the work is a generalized model of a dynamo system, with an additive addition of a random correction to the $\alpha$-generator. Taking into account such a correction significantly diversifies the dynamic modes in the model.
Keywords: hydromagnetic dynamo, memory, heredity, integro-differential equations, stochastic model, coherent structures.
Mots-clés : $\alpha$-effect 
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     author = {E. A. Kazakov and G. M. Vodinchar},
     title = {Stochastic two-mode hereditary model of a cosmic dynamo},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {70--82},
     publisher = {mathdoc},
     volume = {48},
     number = {3},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2024_48_3_a5/}
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E. A. Kazakov; G. M. Vodinchar. Stochastic two-mode hereditary model of a cosmic dynamo. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 48 (2024) no. 3, pp. 70-82. http://geodesic.mathdoc.fr/item/VKAM_2024_48_3_a5/