Stability analysis of anisotropic Bianchi type I cosmological model

Abstract

Locally Rotationally Symmetric(LRS) Bianchi type I cosmological model interacting with scalar field and exponential potential is presented and phase plane analysis is done in the framework of dynamical systems. Evolution equations are analyzed and reduced to a system of ordinary differential equations which are autonomous by suitable variable transformations. All critical points both hyperbolic and non hyperbolic of the system are listed and their stability properties are analyzed and examined from the cosmological point of view. For non hyperbolic points perturbation theory is applied. Some representations of phase diagrams are shown explicitly.