Abstract
Form the observation of the cosmic microwave background radiation done by WMAP, the physical universe is highly homogeneous and isotropic with tiny anisotropic distribution reflecting the initial anisotropy of the expanding universe. The Bianchi type I space will be adopted along with higher order correction terms as the physical models in charge of the evolution of the anisotropic ally expanding universe. Expanding solutions can be solved accordingly. The evolution of these solutions can be treated as a dynamical system that provides detailed stability analysis of these solutions.
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