where the initial values x 1 , x 0 , y 1 and y 0 are arbitrary nonzero real numbers and the parameters a, b and c are arbitrary real numbers with c ¤ 0. In particular we represent the solutions of some particular cases of this system in terms of Tribonacci and Padovan numbers and we prove the global stability of the corresponding positive equilibrium points. The results obtained here extend those obtained in some recent papers.

In this work we solve in closed form the system of difference equationswhere the initial values x−1, x0, y−1 and y0 are arbitrary nonzero real numbers and the parameters a, b and c are arbitrary real numbers with c = 0. In particular we represent the solutions of some particular cases of this system in terms of Tribonacci and Padovan numbers and we prove the global stability of the corresponding positive equilibrium points. The result obtained here extend those obtained in some recent papers.

In this paper, we give explicit formulas of the solutions of the two general systems of difference equationswhere n ∈ N 0 , f , g : D −→ R are "1 − 1" continuous functions on D ⊆ R, the initial values x −i , y −i , i = 0, 1, 2, 3 are arbitrary real numbers in D and the parameters a, b, c and d are arbitrary real numbers. Our results considerably extend some existing results in the literature.

In this work, we study the behavior of the solutions of following three-dimensional system of difference equations x n+1 = f (yn, y n−1), y n+1 = g(zn, z n−1), z n+1 = h(xn, x n−1) where n ∈ N 0 , the initial values x −1 , x 0 , y −1 , y 0 z −1 , z 0 are positive real numbers, the functions f, g, h : (0, +∞) 2 → (0, +∞) are continuous and homogeneous of degree zero. By proving some general convergence theorems, we have established conditions for the global stability of the corresponding unique equilibrium point. We give necessary and sufficient conditions on existence of prime period two solutions of the above mentioned system. Also, we prove a result on oscillatory solutions. As applications of the obtained results, some particular systems of difference equations defined by homogeneous functions of degree zero are investigated. Our results generalize some existing ones in the literature.