On a solvable system of difference equations of higher-order with period two coefficients

Abstract

We show that the next di¤erence equations system x n+1 = anx n k+1 y n k yn n + n+1 ; y n+1 = bny n k+1 x n k xn n + n+1 ; n 2 N 0 ; where N 0 = N [ f0g, the sequences (an) n2N 0 , (bn) n2N 0 , (n) n2N 0 , (n) n2N 0 are two periodic and the initial conditions x i , y i i 2 f0; 1; : : : ; kg, are nonzero real numbers, can be solved. Also, we investigate the behavior of solutions of above mentioned system when a 0 = b 1 and a 1 = b 0 .

Qualitative Behavior of Solutions of Tenth-Order Recursive Sequence Equation

“…For more articles in this direction, we refer the reader to [8][9][10][11][12][13][14] and references cited therein.…”

Solutions formulas for some general systems of difference equations

“…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. One can find in the literature a lot of works on difference equations where explicit formulas of the solutions are given, see for instance [1], [2], [5], [8], [9], [10], [7], [12], [11], [13], [16], [15], [14], [17], [18], [21], [20], [22]. Such type of difference equations and systems is called solvable difference equations.…”

On eight solvable systems of difference equations in terms of generalized Padovan sequences

“…where the sequences p n , q n , r n , s n are some of the sequences x n and y n and k, l are fixed natural numbers. There are studies related to some special cases of the system (1.7) (see, for example, [1,12,20,22]). Motivated by this line of investigations, here we show that the systems of difference equations…”