Qualitative study of anisotropic cosmologies with inhomogeneous equation of state

We examine the qualitative features of anisotropic models sourced by the fluid having an inhomogeneous equation of state (EoS). In particular, we study the asymptotic behavior and cosmic dynamics of the locally rotationally symmetric Bianchi I, Bianchi III and the Kantowski–Sachs spacetime by using the dynamical system technique. The dark energy yielded by the inhomogeneous EoS leads to the accelerated expansion of the universe with vanishing shear at late-times. We further extract the geometrical and physical features of the cosmological dynamical system by rewriting the statefinder diagnostic and cosmographic parameters in terms of its dynamical variables. The model parameters are constrained for the quintessence and phantom evolution of universe. On the basis of model parameter values, the Kantowski–Sachs model undergoes synchronous bounce during its evolution.