# Vestnik КRAUNC. Fiz.-Mat. nauki. 2023. vol. 45. no. 4. P. 52-66. ISSN 2079-6641

**MATHEMATICAL MODELLING **

https://doi.org/10.26117/2079-6641-2023-45-4-52-66

Research Article

Full text in Russian

MSC 34D08, 76W05

**Chaotic Modes in the Low-Mode Model \alpha\Omega-Dynamo with Hereditary \alpha-Quenching by the Field Energy**

**O. V. Sheremetyeva^\ast**

Institute of Cosmophysical Research and RadioWave Propagation, Far Eastern Branch of the Russian Academy of Sciences, 684034 Kamchatka region, Elizovskiy district, Paratunka, Mirnaya str., 7, Russia

Abstract. This article considers the conditions under which it is possible to simulate the chaotic regime of the magnetic field in a large-scale model \alpha\Omega-dynamo in a low-mode approximation. The intensity of the \alpha– and \Omega-generators is regulated by the Lorentz force. The quenching of the \alpha-effect is determined by the action of the Lorentz force through a process with hereditarity properties (finite «memory»). The nature of the impact of the process is determined by an alternating kernel with variable damping frequency and damping coefficient. The effect of large-scale and turbulent generators on the magnetohydrodynamic system is embedded in the control parameters — the Reynolds number and the measure of the \alpha-effect, respectively. Within the framework of this work, the solutions of the magnetohydrodynamic system are investigated for Lyapunov stability in the vicinity of the rest point, depending on the set values of the input parameters. Based on the results of the numerical experiment, the limitations of the stability characteristic and parameters of the system are determined, under which it is possible to simulate the chaotic regime of the magnetic field.

*Key words: \alpha\Omega-dynamo, hereditarity, \alpha-quenching, low-mode dynamo model, magnetic field, chaotic regime, reversals.*

Received: 26.11.2023; Revised: 12.12.2023; Accepted: 13.12.2023; First online: 14.12.2023

**For citation.** Sheremetyeva O. V. Chaotic modes in the low-mode model \alpha\Omega-dynamo with hereditary \alpha\alpha-quenching by the field energy. Vestnik KRAUNC. Fiz.-mat. nauki. 2023, 45: 4, 52-66. EDN: WJOTLU. https://doi.org/10.26117/2079-6641-2023-45-4-52-66.

**Funding.** The work was carried out within the framework of realization of the State task AAAA-A21-121011290003-0.

**Competing interests.** There are no conflicts of interest regarding authorship and publication.

**Contribution and Responsibility.** The author participated in the writing of the article and is fully responsible for submitting the final version of the article to the press.

^\astCorrespondence: E-mail: sheremeteva@ikir.ru

The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Sheremetyeva O. V., 2023

© Institute of Cosmophysical Research and Radio Wave Propagation, 2023 (original layout, design, compilation)

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#### Information about author

**Sheremetyeva Olga Vladimirovna** – Cand.Sci.(Tech.), Research Scientist, Laboratory of Physical Process Modeling, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, Paratunka, Kamchatka, Russia, ORCID 0000-0001-9417-9731.