  We study a new type of magnetoconvection in a nonuniform rotating plasma
layer under a constant vertical magnetic field. To describe the weakly
nonlinear stage of convection we apply Galerkin-truncated approximation and we
obtain the system of equations of Lorentz type. A numerical analysis of these
equations shows the presence of chaotic behavior of convective flows. Criteria
for the appearance of chaotic motions are found depending on the convection
parameters (Rayleigh number $\textrm{Ra}$), magnetic field (Chandrasekhar
number $\textrm{Q}$), rotation (Taylor number $\textrm{Ta}$) for the Keplerian
angular velocity profile $(\textrm{Ro}=-3/4)$ of the medium.
