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.

In this paper, we introduce the generalized hyperbolic Pell numbers over the bidimensional Clifford algebra of hyperbolic numbers. As special cases, we deal with hyperbolic Pell and hyperbolic Pell–Lucas numbers. We present Binet’s formulas, generating functions and the summation formulas for these numbers. Moreover, we give Catalan’s, Cassini’s, d’Ocagne’s, Gelin–Cesàro’s, Melham’s identities and present matrices related to these sequences.

In this study, we establish the binomial transform of the generalized third-order Jacobsthal sequence. We also describe the binomial transform of four special cases of third-order Jacobsthal sequence such as the binomial transform of the third-order Jacobsthal, third-order Jacobsthal–Lucas, modified third-order Jacobsthal–Lucas, third-order Jacobsthal–Perrin sequences. Moreover, we examine their features in more detail.

Bu makalede, bazı rasyonel fark denklemlerinin ayarlanmış Jacobsthal-Padovan sayıları ile çözümlerinin formunu elde ediyoruz. Kesin çözümler ile ayarlanmış Jacobsthal-Padovan sayıları arasında bir ilişki buluyoruz. Literatürün dışında, çözümlerin bu iyi bilinen diziler ile ilişkili kapalı formunu üstel fonksiyonlar kullanarak veriyoruz. Ayrıca, bu fark denklemlerinin denge noktasının asimptotik davranışını inceliyoruz.

Our aim in this paper is to deal with the dynamics of following higher order difference equationwhere A, B > 0, and initial values are positive, and m = {1, 2, ...}. Furthermore, we discuss the periodicity, boundedness, semi-cycles, global asymptotic stability of solutions of these equations.We also handle the rate of convergence of solutions of these difference equations.