The main problem in the study of dynamical systems arising in applications is to determine the asymptotic behavior of the solutions. In mathematical ecology, this problem is related to the study of the persistence of the species. For instance, if there exists a globally asymptotically stable steady state of positive coordinates, then the system is persistent. On the other hand, in most applications the dynamics of different variables of a system of ordinary differential equations are hierarchically scaled: for instance, in ecological models, often, the prey multiply much faster than the predators. Hence, the study and management of systems with various time scales were considered by many authors and remain a high point of interest both from theoretical and practical points of view . properties of solutions of such systems can be studied by using singular perturbation theory or Tikhonov's theory. this thesis, can be divided into three main parts. In the first part, we start with a brief introduction to slow-fast systems and Tikhonov's theory. Slow manifold slow and fast subsystems are defined and notion of canard and delayed loss of stability are introduced. A slow-fast ordinary differential equation (ODE) is customarily written in the form where components of are called fast variables, while those of are called slow variables. In second part, we introduced a ltr"