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Dynamical Behavior of Solutions to Higher-Order System of Fuzzy Difference Equations

Yıl 2025, Cilt: 8 Sayı: 2, 88 - 103, 30.06.2025

Osman Topan , Yasin Yazlik , Sevda Atpınar

https://doi.org/10.33401/fujma.1564113

Öz

In this paper, we concentrate on the global behavior of the fuzzy difference equations system with higher order \begin{eqnarray}\nonumber \alpha_{n+1}=\tau_1+\frac{\alpha_n}{\sum_{i=1}^{m}\beta_{n-i}}, \beta_{n+1}=\tau_2+\frac{\beta_n}{\sum_{i=1}^{m}\alpha_{n-i}}, \quad n\in \mathbb{N}_0, \end{eqnarray} where $\alpha_n, \beta_n$ are positive fuzzy number sequences, parameters $\tau_1, \tau_2$ and the initial values $\alpha_{-i}, \beta_{-i}, i \in \{0, 1, \dots, m\}$, are positive fuzzy numbers. Firstly, we show the existence and uniqueness of the positive fuzzy solution to the mentioned system. Furthermore, we are searching for the boundedness, persistence and convergence of the positive solution to the given system. Finally, we give some numerical examples to show the efficiency of our results.

Anahtar Kelimeler

Fuzzy difference equations system Positive fuzzy solution Dynamical behavior

Kaynakça

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Yıl 2025, Cilt: 8 Sayı: 2, 88 - 103, 30.06.2025

Osman Topan , Yasin Yazlik , Sevda Atpınar

https://doi.org/10.33401/fujma.1564113

Öz

Kaynakça

  • [1] R. DeVault, G. Ladas and S.W. Schultz, On the recursive sequence $x_{n+1}=\frac{A}{x_{n}}+\frac{1}{x_{n-2}}$, Proc. Am. Math. Soc., 126(1998), 3257-3261. $ \href{https://doi.org/10.1090/S0002-9939-98-04626-7}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/0011873183}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000076507700018}{\mbox{[Web of Science]}} $
  • [2] R.M. Abu-Saris and R. DeVault, Global stability of $y_{n+1}=A+\frac{y_{n}}{y_n-k}$, Appl. Math. Lett., 16(2) (2003), 173-178. $ \href{https://doi.org/10.1016/S0893-9659(03)80028-9}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/84867936459}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000181367800008}{\mbox{[Web of Science]}} $
  • [3] G. Papaschinopoulos and C.J. Schinas, On a system of two nonlinear difference equations, J. Math. Anal., 219(2) (1998), 415-426. $ \href{https://doi.org/10.1006/jmaa.1997.5829}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/0000475245}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000072521800014}{\mbox{[Web of Science]}}$
  • [4] Q. Zhang, W. Zhang, Y. Shao and J. Liu, On the system of high order rational difference equations, Int. Sch. Res. Notices, 2014(1) (2014), 760502. $ \href{http://dx.doi.org/10.1155/2014/760502}{\mbox{[CrossRef]}} $
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  • [6] M.R.S. Kulenovic and G. Ladas, Dynamics of Second Order Rational Difference Equations: with Open Problems and Conjectures, Chapman and Hall CRC Press: Boca Raton, FL, USA. $ \href{https://doi.org/10.1201/9781420035384}{\mbox{[CrossRef]}} $
  • [7] V. Lakshmikantham and D. Trigiante, Theory of Difference Equations Numerical Methods and Applications, Marcel Dekker, New York, (2002). $\href{https://doi.org/10.1201/9780203910290}{\mbox{[CrossRef]}} $
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  • [9] M. Gümüş, Global asymptotic behavior of a discrete system of difference equations with delays, Filomat, 37(1) (2023), 251-264. $ \href{https://doi.org/10.2298/FIL2301251G}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85146825142&origin=resultslist&sort=plf-f&src=s&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Global+asymptotic+behavior+of+a+discrete+system+of+difference+equations+with+delays%22%29&sessionSearchId=777e8879f7c059438ed77a63f94881e0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000932858000020}{\mbox{[Web of Science]}} $
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Toplam 34 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik (Diğer)
Bölüm Makaleler
Yazarlar

Osman Topan 0000-0003-0977-4777

Yasin Yazlik 0000-0001-6369-540X

Sevda Atpınar 0000-0003-2589-8331

Yayımlanma Tarihi 30 Haziran 2025
Gönderilme Tarihi 9 Ekim 2024
Kabul Tarihi 13 Kasım 2024
Yayımlandığı Sayı Yıl 2025 Cilt: 8 Sayı: 2

Kaynak Göster

APA Topan, O., Yazlik, Y., & Atpınar, S. (2025). Dynamical Behavior of Solutions to Higher-Order System of Fuzzy Difference Equations. Fundamental Journal of Mathematics and Applications, 8(2), 88-103. https://doi.org/10.33401/fujma.1564113
AMA Topan O, Yazlik Y, Atpınar S. Dynamical Behavior of Solutions to Higher-Order System of Fuzzy Difference Equations. Fundam. J. Math. Appl. Haziran 2025;8(2):88-103. doi:10.33401/fujma.1564113
Chicago Topan, Osman, Yasin Yazlik, ve Sevda Atpınar. “Dynamical Behavior of Solutions to Higher-Order System of Fuzzy Difference Equations”. Fundamental Journal of Mathematics and Applications 8, sy. 2 (Haziran 2025): 88-103. https://doi.org/10.33401/fujma.1564113.
EndNote Topan O, Yazlik Y, Atpınar S (01 Haziran 2025) Dynamical Behavior of Solutions to Higher-Order System of Fuzzy Difference Equations. Fundamental Journal of Mathematics and Applications 8 2 88–103.
IEEE O. Topan, Y. Yazlik, ve S. Atpınar, “Dynamical Behavior of Solutions to Higher-Order System of Fuzzy Difference Equations”, Fundam. J. Math. Appl., c. 8, sy. 2, ss. 88–103, 2025, doi: 10.33401/fujma.1564113.
ISNAD Topan, Osman vd. “Dynamical Behavior of Solutions to Higher-Order System of Fuzzy Difference Equations”. Fundamental Journal of Mathematics and Applications 8/2 (Haziran 2025), 88-103. https://doi.org/10.33401/fujma.1564113.
JAMA Topan O, Yazlik Y, Atpınar S. Dynamical Behavior of Solutions to Higher-Order System of Fuzzy Difference Equations. Fundam. J. Math. Appl. 2025;8:88–103.
MLA Topan, Osman vd. “Dynamical Behavior of Solutions to Higher-Order System of Fuzzy Difference Equations”. Fundamental Journal of Mathematics and Applications, c. 8, sy. 2, 2025, ss. 88-103, doi:10.33401/fujma.1564113.
Vancouver Topan O, Yazlik Y, Atpınar S. Dynamical Behavior of Solutions to Higher-Order System of Fuzzy Difference Equations. Fundam. J. Math. Appl. 2025;8(2):88-103.
 Kapak Resmi İndir

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