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Journals / Communications in Advanced Mathematical Sciences / 2023 / Cilt: 6 Sayı: 1

Global Asymptotic Stability of a System of Difference Equations with Quadratic Terms

Mohamed ABD EL-MONEAM
Pages
31–43
Publication Date
2023-03-31
DOI
—
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AI Summary & Key Takeaways

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

We will give also, some numerical examples to illustrate our results.

📌 3 Key Takeaways

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Objective & Hypothesis:In this article, we discuss the global asymptotic stability of following system of difference equations with quadratic terms: $x_{i+1}=\alpha+\beta \frac{y_{i-1}}{y_{i}^{2}},\quad y_{i+1}=\alpha+\beta \frac{x_{i-1}}{x_{i}^{2} }$ where $\alpha$, $\beta$ are positive numbers and the initial values are positive numbers.
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Key Findings & Data:We also study the rate of convergence and oscillation behaviour of the solutions of related system.
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Conclusion & Impact:We will give also, some numerical examples to illustrate our results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:difference equations · Global asymptotic stability · system

Abstract

In this article, we discuss the global asymptotic stability of following system of difference equations with quadratic terms: $x_{i+1}=\alpha+\beta \frac{y_{i-1}}{y_{i}^{2}},\quad y_{i+1}=\alpha+\beta \frac{x_{i-1}}{x_{i}^{2} }$ where $\alpha$, $\beta$ are positive numbers and the initial values are positive numbers. We also study the rate of convergence and oscillation behaviour of the solutions of related system. We will give also, some numerical examples to illustrate our results.

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Cite This Article

EL-MONEAM, M. A. (2023). Global Asymptotic Stability of a System of Difference Equations with Quadratic Terms. Communications in Advanced Mathematical Sciences, Cilt: 6 Sayı: 1, 31–43. https://ajindex.com/articles/903610

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