Hereditary Oscillator Associated with the Model of a Large-Scale ?? -Dynamo

Gleb Vodinchar
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Gleb Vodinchar: Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, 7, Mirnaya Str., 684034 Paratunka, Kamchatka, Russia

Mathematics, 2020, vol. 8, issue 11, 1-16

Abstract: Cosmic magnetic fields possess complex time dynamics. They are characterized by abrupt polarity changes (reversals), fluctuations of fixed polarity, bursts and attenuations. These dynamic conditions can replace each other, including both regular and chaotic components. Memory in dynamo systems manifests itself in a feedback mechanism when a strong magnetic field begins to change the properties of turbulent flows. A hereditary oscillator can be the simplest model of such complex oscillatory systems with memory. The article suggests the construction of such oscillator by means of two-mode approximation of magnetic field components in the α ω -dynamo model. The hereditary member describes the suppression of a field turbulent generator by magnetic helicity and determines the shape of oscillator potential. The article describes the implicit difference scheme for numerical research of oscillator. It also describes the results of numerical simulation for two cases—instantaneous feedback and delay in feedback. The results of simulation are interpreted in terms of oscillator theory. It is shown that the observed dynamic regimes in the model go well with the change of potential shape.

Keywords: complex oscillatory systems; systems with memory; hydromagnetic dynamo; hereditary oscillators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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