Dynamical system analysis of Einstein–Skyrme model in a Kantowski–Sachs spacetime

Abstract

We consider a Skyrme fluid with a constant radial profile in locally rotational Kantowski-Sachs spacetime. We choose a suitable change of variable so that the Field equations modified to an autonomous system. Then we finds the critical points and inspect the stability of them. Finally, the flow on the Poincaré sphere is shown and consequently the behavior at infinity is determined. To analyze the non-hyperbolic critical points Center Manifold Theory has been used. Possible bifurcation scenarios also have been explained. 95.35.+d, 95.36.+x

Dynamical system analysis of self-interacting three-form field cosmological model: stability and bifurcation

“…In Ref. [11] the autonomous system [19][20][21] is identical to our autonomous system (22)(23)(24), but they have determined few critical points and have analyzed only one critical point by center manifold theory. On the other hand, we have determined all possible critical points both for interacting and non-interacting cases.…”

“…They have not employed center manifold theory nor have discussed global stability for any critical point. Therefore, present work is rich in dynamical system analysis and have studied various cosmic scenarios with reference to cosmic phase transition using bifurcation analysis [22][23][24].…”

“…Now we shall study the stability analysis for interacting model with α as arbitrary parameter. For this case we con-sider the primary autonomous system (22)(23)(24). The critical points for this autonomous system are:…”

“…After shifting the critical point P 4 to the origin and by using same transformation as above the autonomous system (22)(23)(24) changes to…”

“…The calculation change the system of equations (22)(23)(24) due to this coordinate transformation is shown in Appendix B. The Jacobian matrix at the origin for this autonomous system can be written as…”