  The research is devoted to the stability of convective flow in a nonuniformly
rotating layer of an electrically conducting fluid in a spiral magnetic field.
The stationary and oscillatory modes of magnetic convection are considered
depending on the profile of the angular rotation velocity (Rossby number
$\textrm{Ro}$) and on the profile of the external azimuthal magnetic field
(magnetic Rossby number $\textrm{Rb}$). The nonlinear dynamic system of Lorentz
type equations is obtained by using the Galerkin method. Numerical analysis of
these equations has shown the presence of chaotic behavior of convective flows.
The criteria of the occurrence of chaotic movements are found. It depends on
the parameters of convection: dimensionless numbers of Rayleigh $\textrm{Ra}$,
Chandrasekhar $\textrm{Q}$, Taylor $\textrm{Ta}$, and external azimuthal
magnetic field with the Rossby magnetic number $\textrm{Rb}=-1$ for Rayleigh
$(\textrm{Ro}=-1)$ and Kepler $(\textrm{Ro}=-3/4)$ profiles of the angular
rotation velocity of the medium.
