The dynamical analysis of the LRS Bianchi type IV cosmological model

Abstract

In this paper, the LRS Bianchi type IV cosmological model, which is reduced to a second order differential equation, was analyzed in the phase space. The Hubble constant was calculated by using numerical analysis method for the LRS Bianchi type IV cosmological model. We demonstrated that the LRS Bianchi type IV model has oscillatory solutions for the negative energy densities in the interval of - 3.2 <= mu(0) < 0, and the EoS parameter w = +2/3. The initial condition of the cosmic scale factor was selected as A (0) = 1 and angstrom (0) = 0. Here, there is a fixed point of the model for mu(0) = -1.3. Only under these conditions, the model has both oscillatory behaviors and a fixed point. Furthermore, the cyclic attractors of the oscillatory solutions were plotted and the stability properties of the model were discussed in terms of some cosmological models in the context of dynamical systems.