On the periodic solutions of some systems of higher order difference equations

Abstract

In this paper, we obtain the general form of the periodic solutions of some higher order difference equations systemwhere the initial values are arbitrary real numbers such that the denominator is always nonzero. Moreover, some numerical examples are presented to verify our theoretical results. 2010 AMS Mathematics subject classification. Primary 39A10. Keywords and phrases. Periodicity, systems of higher order difference equations, form of the solutions.

Dynamical behavior of a system of three-dimensional nonlinear difference equations

“…Hence, every positive solution {(x n , y n , z n )} of system (6) tends to the positive equilibrium system (6). So, the proof is completed.…”

“…In [6], Göcen and Cebeci studied the general form of periodic solutions of some higher order systems of difference equations…”

“…Theorem 8 Assume that 0 < A < 1 and {(x n , y n , z n )} is an arbitrary positive solution of system (6). Then the following statements are true.…”

On some classes of solvable systems of difference equations

“…Many of our papers are also devoted to the area (see, e.g., [17,23,24,27,29,32,33,36] and the references therein). For other related results, including the ones on invariants of difference equations, see, e.g., [39,40,43,45,46] and the references therein. Let us also mention that some more complex solvable difference equations and systems can be found, e.g., in [17,33,[47][48][49][50][51], but the idea is essentially the same as in the above-mentioned papers, that is, some connections of studied difference equations and systems to some solvable ones are found.…”

“…In recent paper [46] periodicity of well-defined solutions to the following systems of difference equations has been studied:…”