On some systems of difference equations, solutions form, stability and periodicity

Abstract

This thesis concerns the study of certain classes of systems of nonlinear difference equations where each time we present the solutions on the closed form. In the first chapter, we study systems of difference equations with different degrees, where we have presented the solutions using well-known number sequences such as, Fibonacci numbers, Padovan, Tribonacci and generalized Tribonacci numbers. The second chapter is devoted to the study and the resolution of a system of three difference equations defined by homogeneous functions. As for the third and fourth chapter, we presented a study of higher-order of system of three difference equations and a two dimensional Max-type system of difference equations. Each time, we present the explicit form of the solutions, and a qualitative study of the solutions and their equilibrium points of some particular cases is discussed, including convergence, local and global asymptotic stability, as well as periodicity and oscillatory