  We consider a low-dimensional model of convection in a horizontally
magnetized layer of a viscous fluid heated from below. We analyze in detail the
stability of hydromagnetic convection for a wide range of two control
parameters. Namely, when changing the initially applied temperature difference
or magnetic field strength, one can see transitions from regular to irregular
long-term behavior of the system, switching between chaotic, periodic, and
equilibrium asymptotic solutions. It is worth noting that owing to the induced
magnetic field a transition to hyperchaotic dynamics is possible for some
parameters of the model. We also reveal new features of the generalized Lorenz
model, including both type I and III intermittency.
