Dynamics of generation modes changes in magnetic field depending on the oscillation frequency of the $\alpha$-effect suppression process by field energy in the $\alpha\Omega$-dynamo model

This article considers a $\alpha\Omega$-dynamo large-scale model in a low-mode approximation. The intensity of the $\alpha$-effect is regulated by a process with hereditarity properties, depending on the energy of the magnetic field. The nature of the process impact is determined by an alternating kernel function with a variable damping frequency and a constant damping coefficient equal to 0.1. Based on the results of numerical simulation of the magnetic field generation modes, the boundaries for the values of the model parameters are determined for which there are no oscillations in the velocity field of a viscous liquid or they are insignificant. The results of magnetic field generation modes simulation at various damping frequency values are displayed on the phase plane of the control parameters. These parameters contain information about large-scale and turbulent generators. The paper investigates the question about the dynamics of changes in the pattern on the phase plane depending on the value of the damping frequency and the waiting time. A comparison is made with the results obtained earlier for the constant intensity of the $\alpha$-effect and for the intensity, the change of which is determined by the process with exponential kernel.