Abstract
The present work deals with anisotropic (but zero heat flux) Skyrme fluid with a constant radial profile in locally rotational Kantowski–Sachs spacetime in the background of Einstein gravity. By suitably change of variables the field equations are transformed to an autonomous system. To examine the stability of the system critical points are determined. For hyperbolic critical points the analysis of the system is done using Hartman–Grobman theorem, while center manifold theory is used to analyze non-hyperbolic critical points. Also stability at infinity is analyzed to visualize the global evolution of the Universe. As a result the 3D-phase space is identified with the Poincaré 3-sphere embedded in R4. It is found that the parameters in the autonomous system play a crucial role for phase transition of the Universe. Finally possible bifurcation scenarios are discussed to identify the point of phase transition.
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