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Journals / Gazi University Journal of Science / 2026 / Volume: 38 Issue: 1

Dynamic Behavior of a Fourth-Order Nonlinear Fuzzy Difference Equation

İbrahim Yalçınkaya(NECMETTIN ERBAKAN UNIVERSITY)0000-0003-4546-4493
Bilal Er(TC MİLLİ EĞİTİM BAKANLIĞI)0000-0003-2461-3330
Durhasan Turgut Tollu(Necmettin Erbakan University)0000-0002-3313-8829
Pages
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Publication Date
2025-03-01
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⚡ TL;DR(Too Long; Didn't Read)

In this paper we investigate the existence, the boundedness and the asymptotic behavior of the positive solutions of the fuzzy difference equation w_{n+1}=((Aw_{n-1})/(B+Cw_{n-3}^{p})), n∈ℕ₀, where (w_{n}) is a sequence of positive fuzzy numbers, the parameters A, B, C and the initial conditions w₋₃, w₋₂, w₋₁, w₀ are positive fuzzy numbers and p is a positive integer.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper we investigate the existence, the boundedness and the asymptotic behavior of the positive solutions of the fuzzy difference equation w_{n+1}=((Aw_{n-1})/(B+Cw_{n-3}^{p})), n∈ℕ₀, where (w_{n}) is a sequence of positive fuzzy numbers, the parameters A, B, C and the initial conditions w₋₃, w₋₂, w₋₁, w₀ are positive fuzzy numbers and p is a positive integer.
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Key Findings & Data:In this paper we investigate the existence, the boundedness and the asymptotic behavior of the positive solutions of the fuzzy difference equation w_{n+1}=((Aw_{n-1})/(B+Cw_{n-3}^{p})), n∈ℕ₀, where (w_{n}) is a sequence of positive fuzzy numbers, the parameters A, B, C and the initial conditions w₋₃, w₋₂, w₋₁, w₀ are positive fuzzy numbers and p is a positive integer.
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Conclusion & Impact:In this paper we investigate the existence, the boundedness and the asymptotic behavior of the positive solutions of the fuzzy difference equation w_{n+1}=((Aw_{n-1})/(B+Cw_{n-3}^{p})), n∈ℕ₀, where (w_{n}) is a sequence of positive fuzzy numbers, the parameters A, B, C and the initial conditions w₋₃, w₋₂, w₋₁, w₀ are positive fuzzy numbers and p is a positive integer.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Asymptotic behavior · α-cuts · Boundedness

Abstract

In this paper we investigate the existence, the boundedness and the asymptotic behavior of the positive solutions of the fuzzy difference equation w_{n+1}=((Aw_{n-1})/(B+Cw_{n-3}^{p})), n∈ℕ₀, where (w_{n}) is a sequence of positive fuzzy numbers, the parameters A, B, C and the initial conditions w₋₃, w₋₂, w₋₁, w₀ are positive fuzzy numbers and p is a positive integer.

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Cite This Article

Yalçınkaya, İ., Er, B., Tollu, D. T. (2025). Dynamic Behavior of a Fourth-Order Nonlinear Fuzzy Difference Equation. Gazi University Journal of Science, Volume: 38 Issue: 1. https://doi.org/10.35378/gujs.1098124

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