The paper "Determination of dynamic modes in hereditary two-mode dynamo model" has been published

The scientific paper of the Junior Researcher of the Laboratory of Electromagnetic Radiation, Kazakov E.A., and the Leading Researcher of the Laboratory of Physical Process Modeling, Cand. of Sci. (Phys.-Math.) Vondinchar G.M., has been published in the Journal "Bulletin of Samara State Technical University. Series: Physical-Mathematical Sciences".

The paper is devoted to the analysis of the results of computational experiments with a hereditary dynamic system modeling two-mode hydromagnetic dynamo with memory. The paper investigates numerically the dynamic modes occurring during variation of the control parameters of this system. The hereditary dynamic system is represented in the form of a system of integro-differential equations.

One of the key methods for investigating the dynamic modes is analysis of Lyapunov exponents. To apply this method, the integro-differential equation system was reduced to a system of ordinary differential equations. The paper describes the corresponding class of cores and the reduction result.

As an alternative approach, 0-1 test was used to determine the dynamic modes. The results, obtained by 0-1 test and Lyapunov exponents for a special case, were compared and showed their qualitative correspondence. In further investigation of the dynamic modes of the integro-differential system, 0-1 test was mainly applied.

Cases of both instantaneous and delayed hereditary feedback were under investigation. The modeling results show that the considered model reproduces a series of dynamic modes typical for real space dynamo systems.

The paper in Russian is available at the link.

For the reference: E.A. Kazakov, G.M. Vodinchar “Determination of dynamic modes in a hereditary two-mode dynamo model”, Bulletin of Samara State Technical University. Series: Physical-Mathematical Sciences, 29:2 (2025), 319–333, DOI: https://doi.org/10.14498/vsgtu2130