Dynamics of a High-Order Generalized Lorenz Model for Magnetoconvection

Abstract

In this paper, we present a 6D generalized Lorenz model for magnetoconvection of an electrically conducting viscous fluid layer subjected to horizontally imposed uniform magnetic field. It generalizes the 4D generalized Lorenz model of Macek and Strumik [Phys. Rev. E 82, 027301 (2010)] taking into account high-wavenumber vertical Fourier modes of the temperature profile. These additional modes not only increase the feedback loop of the system but also subsequently affect the transitional processes. The boundedness, stability of solutions, bifurcation patterns enroute to chaos for the new 6D model are explored. Studies reveal that the stability of the quiescent state does not alter. But the stability of the steady convective state differs in comparison to the 4D model. The regions of aperiodic oscillation are suppressed which results in stabilization of the convective motion. Some new organized periodic structures embedded in chaotic domain appear in parameter space of the 6D model, and the transitional route to hyperchaos is altered owing to the inclusion of the high-order modes.