  Assuming a large-scale homogeneous magnetic field, we follow the covariant
and gauge-invariant approach used by Tsagas and Barrow to describe the
evolution of density and magnetic field inhomogeneities and curvature
perturbations in a matter-radiation universe. We use a two parameter
approximation scheme to linearize their exact non-linear general-relativistic
equations for magneto-hydrodynamic evolution. Using a two-fluid approach we set
up the governing equations as a fourth order autonomous dynamical system.
Analysis of the equilibrium points for the radiation dominated era lead to
solutions similar to the super-horizon modes found analytically by Tsagas and
Maartens. We find that a study of the dynamical system in the dust-dominated
era leads naturally to a magnetic critical length scale closely related to the
Jeans Length. Depending on the size of wavelengths relative to this scale,
these solutions show three distinct behaviours: large-scale stable growing
modes, intermediate decaying modes, and small-scale damped oscillatory
solutions.
