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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In this paper, we investigated the periodic nature and the form of the solutions of nonlinear dierence equations systems of order three$$x_{n+1}=\dfrac{x_{n-2}y_{n-1}}{y_n(\pm 1\pm x_{n-2}y_{n-1})}, y_{n+1}=\dfrac{y_{n-2}x_{n-1}}{x_n(\pm 1\pm y_{n-2}x_{n-1})},$$ with initial conditions $x_{-2}, x_{-1}, x_0,y_{-2}, y_{-1}$ and $y_0$ are nonzero real numbers.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we investigated the periodic nature and the form of the solutions of nonlinear dierence equations systems of order three$$x_{n+1}=\dfrac{x_{n-2}y_{n-1}}{y_n(\pm 1\pm x_{n-2}y_{n-1})}, y_{n+1}=\dfrac{y_{n-2}x_{n-1}}{x_n(\pm 1\pm y_{n-2}x_{n-1})},$$ with initial conditions $x_{-2}, x_{-1}, x_0,y_{-2}, y_{-1}$ and $y_0$ are nonzero real numbers.
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Key Findings & Data:In this paper, we investigated the periodic nature and the form of the solutions of nonlinear dierence equations systems of order three$$x_{n+1}=\dfrac{x_{n-2}y_{n-1}}{y_n(\pm 1\pm x_{n-2}y_{n-1})}, y_{n+1}=\dfrac{y_{n-2}x_{n-1}}{x_n(\pm 1\pm y_{n-2}x_{n-1})},$$ with initial conditions $x_{-2}, x_{-1}, x_0,y_{-2}, y_{-1}$ and $y_0$ are nonzero real numbers.
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Conclusion & Impact:In this paper, we investigated the periodic nature and the form of the solutions of nonlinear dierence equations systems of order three$$x_{n+1}=\dfrac{x_{n-2}y_{n-1}}{y_n(\pm 1\pm x_{n-2}y_{n-1})}, y_{n+1}=\dfrac{y_{n-2}x_{n-1}}{x_n(\pm 1\pm y_{n-2}x_{n-1})},$$ with initial conditions $x_{-2}, x_{-1}, x_0,y_{-2}, y_{-1}$ and $y_0$ are nonzero real numbers.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:recursive sequences · stability · periodic solution
Abstract
In this paper, we investigated the periodic nature and the form of the solutions of nonlinear dierence equations systems of order three$$x_{n+1}=\dfrac{x_{n-2}y_{n-1}}{y_n(\pm 1\pm x_{n-2}y_{n-1})}, y_{n+1}=\dfrac{y_{n-2}x_{n-1}}{x_n(\pm 1\pm y_{n-2}x_{n-1})},$$ with initial conditions $x_{-2}, x_{-1}, x_0,y_{-2}, y_{-1}$ and $y_0$ are nonzero real numbers.
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Cite This Article
Elsayed, E. M., İbrahim, T. F. (2022). Periodicity and solutions for some systems of nonlinear rational difference equations. Hacettepe Journal of Mathematics and Statistics, Cilt: 44 - Sayı: 6, 1361–1390. https://ajindex.com/articles/530327