Contribution to the study of the characteristics and dynamic properties of certain classes of nonlineardifference equations

Abstract

Our objective in this thesis is to study the qualitative behavior and the solvability of some nonlinear systems of difference equations. In the first two chapters, we will study several systems of rational difference equations with arbitrary powers. We will focus on the asymptotic behavior of solutions and employ techniques such as linearization, monotonicity, and boundedness to establish conditions for local and global stability of equilibrium points. We will also obtain results concerning the existence of periodic solutions and support them with numerical examples. In the last chapter, we will derive explicit solutions of certain non-autonomous equation and new classes of nonlinear systems of difference equations by applying suitable changes of variables.vv