Bifurcations and Exact Solutions of the Equation of Barotropic FRW Cosmologies

Abstract

In this paper, we study the equation of barotropic Friedmann–Robertson–Walker cosmologies. By using the method of dynamical systems, we obtain bifurcations of the phase portraits of the corresponding planar dynamical system. Corresponding to different level curves, we derive exact explicit parametric representations of bounded and unbounded solutions, such as periodic solutions, periodic peakon solutions, homoclinic and heteroclinic solutions and compacton solutions.