Behavior of solutions of a second order rational difference equation

Abo-Zeid, R.

doi:10.5937/matmor1901011a

Cited by 13 publications

(4 citation statements)

References 23 publications

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“…Hence, we must prove that it is true for 𝑘 + 1. Taking into account ( 8) and (15), as in Theorem 4, similarly, we have…”

Section: The Second Equationmentioning

confidence: 97%

Bazi Fark Denklemleri̇ni̇n Ayarlanmiş Jacobsthal-Padovan Sayilari İle İli̇şki̇li̇ Tam Çözümleri̇

Göcen

2022

Kırklareli Üniversitesi Mühendislik Ve Fen Bilimleri Dergisi

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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.

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“…Hence, we must prove that it is true for 𝑘 + 1. Taking into account ( 8) and (15), as in Theorem 4, similarly, we have…”

Section: The Second Equationmentioning

confidence: 97%

Bazi Fark Denklemleri̇ni̇n Ayarlanmiş Jacobsthal-Padovan Sayilari İle İli̇şki̇li̇ Tam Çözümleri̇

Göcen

2022

Kırklareli Üniversitesi Mühendislik Ve Fen Bilimleri Dergisi

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“…The theory of system of difference equations improved until today. Recently, there has been great interest in studying difference equation or difference equations systems [1][2][3][5][6][7]9,[12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Solvability of a Four Dimensional System of Difference Equations

DEVECİOĞLU,

KARA

2024

Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler

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In this study, we investigate the following four-dimensional difference equations system {█(u_n=(αu_(n-3) t_(n-2)+β)/(γv_(n-1) t_(n-2) u_(n-3) ), @v_n=(αv_(n-3) u_(n-2)+β)/(γw_(n-1) u_(n-2) v_(n-3) ),n∈N_0,@w_n=(αw_(n-3) v_(n-2)+β)/(γt_(n-1) v_(n-2) w_(n-3) ), @t_n=(αt_(n-3) w_(n-2)+β)/(γu_(n-1) w_(n-2) t_(n-3) ), )┤ where the initial values u_(-d),v_(-d),w_(-d),t_(-d), d∈{1,2,3} and the parameters α,β,γ are real numbers. Then, we obtain the solutions of system of third-order difference equations in explicit form. In addition, the solutions according to some special cases of the parameters are examined. Finally, numerical examples are given to demonstrate the theoretical results.

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“…Some of the forms of solutions of these equations are representable via well-known integer sequences such as Fibonacci numbers [1,2], Horadam numbers [3], Lucas numbers [4,5], and Padovan numbers [6]. For more on Fibonacci and Lucas numbers, one can see [7,8], for more on difference equations and systems of difference equations solvable in closed form, one can see [9]- [24].…”

Section: Introductionmentioning

confidence: 99%

Solvability of a Second-Order Rational System of Difference Equations

BERKAL,

ABO-ZEID

2023

Fundamental Journal of Mathematics and Applications

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In this paper, we represent the admissible solutions of the system of second-order rational difference equations given below in terms of Lucas and Fibonacci sequences: \begin{eqnarray*} \begin{split} x_{n+1}=\dfrac{L_{m+2}+L_{m+1}y_{n-1}}{L_{m+3}+L_{m+2}y_{n-1}},\quad y_{n+1}=\dfrac{L_{m+2}+L_{m+1}z_{n-1}}{L_{m+3}+L_{m+2}z_{n-1}},\\ z_{n+1}=\dfrac{L_{m+2}+L_{m+1}w_{n-1}}{L_{m+3}+L_{m+2}w_{n-1}},\quad w_{n+1}=\dfrac{L_{m+2}+L_{m+1}x_{n-1}}{L_{m+3}+L_{m+2}x_{n-1}}. \end{split} \end{eqnarray*} where $n\in\mathbb{N}_0$, $\{L_m\}_{m=-\infty}^{+\infty}$ is Lucas sequence and the initial conditions $x_{-1}$, $x_{0}$, $y_{-1}$, $y_{0}$, $z_{-1}$, $z_{0}$, $w_{-1}$, $w_{0}$ are arbitrary real numbers such that $\displaystyle v_{-i}\neq-\frac{L_{m+3}}{L_{m+2}}$, where $v_{-i}=x_{-i},y_{-i},z_{-i},w_{-i}$, $i=0,1$ and $m\in\mathbb{Z}$.

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Behavior of solutions of a second order rational difference equation

Cited by 13 publications

References 23 publications

Bazi Fark Denklemleri̇ni̇n Ayarlanmiş Jacobsthal-Padovan Sayilari İle İli̇şki̇li̇ Tam Çözümleri̇

Bazi Fark Denklemleri̇ni̇n Ayarlanmiş Jacobsthal-Padovan Sayilari İle İli̇şki̇li̇ Tam Çözümleri̇

Solvability of a Four Dimensional System of Difference Equations

Solvability of a Second-Order Rational System of Difference Equations

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