Dynamics of anisotropic cosmological model with ultrarelativistic matter,magnetic field,and fluxes of free isotropic particles

Within the framework of general relativity a dynamics of homogeneous anistropic axially symmetric model of the Bianchi type I is considered for the case when sources of gravitational field are ultrarelativistic matter, homogeneous magnetic field, and fluxes of free particles. Qualitative analysis of the field equations on a phase plane is given. All solutions of a considered type for large values of proper time asymptotically approach the flat Friedmann model while the value of energy density of free particles approaches the double value of magnetic field energy density. Near a singular state the solution exhibits oscillating behavior with successive interchange of Kasner singularities of pancake-like and filament-like types. It is also shown that in the absence of matter a solution retains its character.