Dynamical systems approach to a Bianchi type I viscous magnetohydrodynamic model

We use the expansion-normalized variables approach to study the dynamics of a nontilted Bianchi type I cosmological model with both a homogeneous magnetic field and a viscous fluid. In our model the perfect magnetohydrodynamic approximation is made, and both bulk and shear viscous effects are retained. The dynamical system is studied in detail through a fixed-point analysis which determines the local sink and source behavior of the system. We show that the fixed points may be associated with Kasner-type solutions, a flat universe Friedmann-LeMaître-Robertson-Walker solution, and interestingly, a new solution to the Einstein field equations involving nonzero magnetic fields and nonzero viscous coefficients. It is further shown that for certain values of the bulk and shear viscosity and equation of state parameters, the model isotropizes at late times.