  In this paper, we discuss the phase space analysis of locally rotationally
symmetric Bianchi type I universe model by taking a noninteracting mixture of
dust like and viscous radiation like fluid whose viscous pressure satisfies a
nonlinear version of the Israel-Stewart transport equation. An autonomous
system of equations is established by defining normalized dimensionless
variables. In order to investigate the stability of the system, we evaluate
corresponding critical points for different values of the parameters. We also
compute the power-law scale factor whose behavior indicates different phases of
the universe model. It is found that our analysis does not provide a complete
immune from fine-tuning because the exponentially expanding solution occurs
only for a a particular range of parameters. We conclude that stable solutions
exist in the presence of nonlinear model for bulk viscosity with different
choices of the constant parameter $m$ for anisotropic universe.
