Chaotic magnetoconvection in a non-uniformly rotating electroconductive fluids

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 $\text{Ra}$), magnetic field (Chandrasekhar number $\text{Q}$), rotation (Taylor number $\text{Ta}$) for the Keplerian angular velocity profile $(\text{Ro}=-3\mathrm{/}4)$ of the medium.