Qualitative Study of Certain Second Order Quadratic Difference Equations

This thesis is dedicated to the study of the qualitative behavior of some classesof non-linear difference equations and system of difference equations. We fo-cused on the study of the boundedness character, the asymptotic stability ofequilibrium points, oscillation, existence of periodic solutions and the globalattractivity about equilibrium points of second order quadratic autonomousrational difference equation as well as the non-autonomous higher order ra-tional difference equation. In addition to that we are interested to solve anopen problem concerning the system of higher order non-autonomous differ-ence equations. As well as another third order non-autonomous system. Asan application of difference equations and their system, we have giving twobiological models. We conclude our work by giving some numerical exampleswhich permit to confirm and illustrate our contributions.