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Journals / Gazi University Journal of Science / 2020 / Cilt: 33 - Sayı: 3

Well-Defined Solutions of a Three-Dimensional System of Difference Equations

Yasin YAZLIK
Merve KARA
Nouressadat TOUAFEK
Pages
767–778
Publication Date
2022-10-19
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Some numericalexamples are given to demonstrate the theoretical results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We show that the three-dimensional system of difference equations𝑥𝑛+1 =𝑎𝑥𝑛𝑧𝑛−1𝑧𝑛−𝛽+ 𝛾, 𝑦𝑛+1 =𝑏𝑦𝑛𝑥𝑛−1𝑥𝑛−𝛾+ 𝛼, 𝑧𝑛+1 =𝑐𝑧𝑛𝑦𝑛−1𝑦𝑛−𝛼+ 𝛽 , 𝑛 ∈ 𝑁0 ,where the parameters 𝑎, 𝑏, 𝑐, 𝛼, 𝛽, 𝛾 and the initial conditions 𝑥−𝑖 , 𝑦−𝑖 , 𝑧−𝑖 , 𝑖 ∈ {0,1}, are nonzeroreal numbers, can be solved.
📊
Key Findings & Data:Using the obtained formulas, we determine the asymptoticbehavior of solutions and give conditions for which periodic solutions exist.
💡
Conclusion & Impact:Some numericalexamples are given to demonstrate the theoretical results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

We show that the three-dimensional system of difference equations𝑥𝑛+1 =𝑎𝑥𝑛𝑧𝑛−1𝑧𝑛−𝛽+ 𝛾, 𝑦𝑛+1 =𝑏𝑦𝑛𝑥𝑛−1𝑥𝑛−𝛾+ 𝛼, 𝑧𝑛+1 =𝑐𝑧𝑛𝑦𝑛−1𝑦𝑛−𝛼+ 𝛽 , 𝑛 ∈ 𝑁0 ,where the parameters 𝑎, 𝑏, 𝑐, 𝛼, 𝛽, 𝛾 and the initial conditions 𝑥−𝑖 , 𝑦−𝑖 , 𝑧−𝑖 , 𝑖 ∈ {0,1}, are nonzeroreal numbers, can be solved. Using the obtained formulas, we determine the asymptoticbehavior of solutions and give conditions for which periodic solutions exist. Some numericalexamples are given to demonstrate the theoretical results.

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Cite This Article

YAZLIK, Y., KARA, M., TOUAFEK, N. (2022). Well-Defined Solutions of a Three-Dimensional System of Difference Equations. Gazi University Journal of Science, Cilt: 33 - Sayı: 3, 767–778. https://ajindex.com/articles/521265

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