Dynamical system analysis of high order gravitation theories

In this thesis, evolution and constraint equations are obtained by using RW metric in Einstein field equations. It is assumed that pressure variable is a function of matter-energy density and barotropic perfect fluid equation of state as well as Modified Chaplygin Gas equation of state are used separately. In order to obtain a dynamical system from these evolution and constraint equations, equations are made dimensionless by defining dimensionless variables. While creating the dynamical systems, it is assumed that $\Lambda$ cosmological constant, Modified Chaplygin Gas and the $\gamma=0$ state that is effectively equivalent to the cosmological constant, which are dark component candidates, could coexist in the universe. Although two-dimensional compact state space could be used for barotropic perfect fluid, in order to obtain extra information about Hubble parameter by using third dimension in the graphic, a noncompact state space is created and it is given alongside the two-dimensional compact state space. When using Modified Chaplygin Gas, Hubble parameter was left out and a compact state space is used, since there are three evolution equations coupled to each other and it is not possible to visualize more than three dimensions in a single state space. When these dinamical systems are examined, unless a restriction is put on Hubble parameter, in other words when contracting and expanding universe models are both possible, it is seen that there is no stable equilibrium point or attractor and universe may continuously evolve from a model to another without the need for a beginning or an end, that is, it has a dynamic structure.