  We analyze the state space of a Bianchi-I universe with anisotropic sources.
Here we consider an extended state space which includes null geodesics in this
background. The evolution equations for all the state observables are derived.
Dynamical systems approach is used to study the evolution of these equations.
The asymptotic stable fixed points for all the evolution equations are found.
We also check our analytic results with numerical analysis of these dynamical
equations. The evolution of the state observables are studied both in cosmic
time and using a dimensionless time variable. Then we repeat the same analysis
with a more realistic scenario, adding the isotropic (dust like dark) matter
and a cosmological constant (dark energy) to our anisotropic sources, to study
their co-evolution. The universe now approaches a de~Sitter space
asymptotically dominated by the cosmological constant. The cosmic microwave
background anisotropy maps due to shear are also generated in this scenario,
assuming that the universe contains anisotropic matter along with the usual
(dark) matter and vacuum (dark) energy since decoupling. We find that they
contribute dominantly to the CMB quadrupole. We also constrain the current
level of anisotropy and also search for any cosmic preferred axis present in
the data. We use the Union~2 Supernovae data to this extent. An anisotropy axis
close to the mirror symmetry axis seen in the cosmic microwave background data
from Planck probe is found.
