On a system of difference equations of second order solved in closed form

Abstract

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.

On the solutions of a system of (2p+1) difference equations of higher order

“…Let k = 1 and p = 2 in system (1.9), then we obtain the system Example 2. Let k = 3 and p = 3 in system (1.9), then we obtain the system (n) X (3) (n) X (4) (n) X (1) (n) X (2) (n) X…”

Solutions formulas for some general systems of difference equations

“…Difference equations are used to describes real discrete models in various branches of modern sciences such as, biology, economy, control theory. This explain why a big number of papers is devoted to this subject, see for example ( [1] - [20]). It is clear that if we want to understand our models, we need to know the behavior of the solutions of the equations of the models, and this fact will be possible if we can solve in closed form these equations.…”

Representation of solutions of a two-dimensional system of difference equations

“…Solvability of difference equations and system of difference equations has attracted considerable interest recently (see, for example [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], and the related references therein).…”