TY  - JOUR
T1  - Periodic Solutions of Some Higher Order Rational Difference Equations
TT  - Bazı Yüksek Mertebeden Rasyonel Fark Denklemlerinin Periyodik Çözümleri
AU  - Göcen, Melih
PY  - 2025
DA  - October
Y2  - 2025
DO  - 10.35414/akufemubid.1569529
JF  - Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi
PB  - Afyon Kocatepe Üniversitesi
WT  - DergiPark
SN  - 2149-3367
SP  - 1091
EP  - 1094
VL  - 25
IS  - 5
LA  - en
AB  - In this paper, the periodicity of the solutions of some higher order difference equationsw_(n+1)=(w_n w_(n-k-1))/w_(n-k) ,       n, k ∈  N_0                        "   "  are investigated where the initial conditions are arbitrary real numbers such that the denominator is always nonzero. While investigating the periodicity of this higher order equation, first the special cases of the equation were considered then a generalization was given for the periodicity of the solution of this higher order difference equation. Moreover, some numerical examples are given to illustrate our theoretical results.
KW  - Periodicity
KW  - difference equations
KW  - positive solutions
KW  - p-cycle
N2  - Bu makalede, başlangıç koşulları paydanın her zaman sıfırdan farklı olacağı şekilde keyfi reel sayılar olmak üzere, bazı yüksek mertebedenw_(n+1)=(w_n w_(n-k-1))/w_(n-k) ,       n,k ∈ N_0                        "   "  fark denklemlerinin çözümlerinin periyodikliği araştırılmıştır. Bu yüksek mertebeden denklemin periyodikliği araştırılırken önce denklemin özel durumları ele alınmış, daha sonra bu yüksek mertebeden fark denkleminin çözümünün periyodikliği için bir genelleme yapılmıştır. Ayrıca teorik sonuçlarımızı göstermek için bazı sayısal örnekler verilmiştir.
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https://doi.org/10.1006/jmaa.1999.6346.
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CR  - Camouzis, E.,  Ladas, G. 2007. Dynamics of third-order rational difference equations with open problems and conjectures. Chapman & Hall/CRC.
CR  - DeVault, R., Kent, C., Kosmala, W. 2003. On the recursive sequence  x_(n+1)=p+x_(n-k)/x_n . Journal of Difference Equations and Applications, 9(8), 721–730. 
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CR  - Göcen, M., Cebeci, A. 2018. On the periodic solutions of some systems of higher order difference equations. Rocky Mountain Journal of Mathematics, 48(3), 845–858. 
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CR  - Göcen, M., Cebeci, A. 2022. Form of the periodic solutions of some systems of higher order  difference equations. Asian-European Journal of Mathematics, 15(2), 2250029 (16 pages). 
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CR  - Göcen, M., Güneysu, M., 2018. The global attractivity of some rational difference equations. Journal of Computational Analysis and Applications, 25(7), 1233-1243.
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CR  - Okumuş, İ., Soykan, Y. 2019. On the Solutions of Four Second-Order Nonlinear Difference Equations. Universal Journal of Mathematics and Applications, 2(3), 116-125. 
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CR  - Taşdemir, E. 2021. Global dynamics of a higher order difference equation with a quadratic term. Journal of Applied Mathematics and Computing, 67(1-2), 423-437. 
https://doi.org/10.1007/s12190-021-01497-x.
CR  - Taşdemir, E., Göcen, M., Soykan, Y. 2022. Global Dynamical Behaviours and Periodicity of a Certain Quadratic-Rational Difference Equation with Delay. Miskolc Mathematical Notes, 23(1), 471-484. 
https://doi.org/10.18514/MMN.2022.3996
UR  - https://doi.org/10.35414/akufemubid.1569529
L1  - https://dergipark.org.tr/tr/download/article-file/4297464
ER  -