Interacting scalar and spinor fields in Bianchi type I universe filled with magneto-fluid

Self-consistent system of spinor, scalar and BI gravitational fields in presence of magneto-fluid and $\Lambda$-term is considered. Assuming that the expansion of the BI universe is proportional to the $\sigma_1^1$ component of the shear tensor, exact solutions for the metric functions, as well as for scalar and spinor fields are obtained. For a non-positive $\Lambda$ the initially anisotropic space-time becomes isotropic one in the process of expansion, whereas, for $\Lambda > 0$ an oscillatory mode of expansion of the BI model occurs.