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Published online by Cambridge University Press: 23 December 2024
Planetary influence on a stellar convective shell can result in a periodic modulation of stellar dynamo drivers. Similar modulation can arise in stellar binary systems. Using the Parker low-mode dynamo model we investigate the properties of nonlinear parametric resonance. This model is a system of four ordinary differential equations and, in the first approximation, describes the processes of generation and oscillation of large-scale magnetic fields in stellar systems. In the absence of nonlinear suppression effects, the problem, by analogy with a system of harmonic oscillations, allows an asymptotic selection of multiple resonant frequencies. Despite the fact that at first glance at these frequencies it is reasonable to expect an increase in the amplitude, the behavior of the system can be just the opposite. All this stuff deserves a systematic analysis of swing excitation in the dynamo sistems in comparison with classical swing excitation in the framework of the Mathieu equation.