Research of the parametric space of the three-mode $\alpha\omega$-dynamo model

In the framework of this work, we study a simple phenomenological model of a $\alpha\omega$-dynamo, with dynamic suppression of a $\alpha$-generator by a quadratic form from a magnetic field component. In particular, suppression of spiralness and energy is available. The shape of the nucleus is determined, and the system of differentiation of the Lorentz type. In general, the models have the possibility of a wide range of functional and quadratic forms. Compared with the classical case of the Lorentz system.