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 $\mathrm{\Lambda }$-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 $\mathrm{\Lambda }$ the initially anisotropic space-time becomes isotropic one in the process of expansion, whereas, for $\mathrm{\Lambda }>0$ an oscillatory mode of expansion of the BI model occurs.