Hereditary low-mode dynamo model

This article discusses a dynamo model in the form of a two-dimensional dynamical system in integro-differential form. The model implements a stabilizing polarization generator in the form of suppression of the a effect of convolutional type functional from current and previous helicity and energy values. The presence of this suppression mechanism introduces hereditarity (memory) into the model. For modeling, a digital scheme was constructed in the form of a combination of difference schemes for the differential and integral parts, a twostep implicit Runge-Kutta method and a trapezium method, respectively. We also reviewed and graphically presented the dynamic modes of our model.