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Dynamic Behavior of a Fourth-Order Nonlinear Fuzzy Difference Equation

Yıl 2025, Cilt: 38 Sayı: 1, 275 - 290, 01.03.2025

İbrahim Yalçınkaya , Bilal Er , Durhasan Turgut Tollu

https://doi.org/10.35378/gujs.1098124

Öz

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.

Anahtar Kelimeler

Asymptotic behavior α-cuts Boundedness Fuzzy difference equation Fuzzy number Stability

Kaynakça

  • [1] Chrysafis, K.A., Papadopoulos, B.K. and Papaschinopoulos, G., “On the fuzzy difference equations of finance”, Fuzzy Sets and Systems, 159: 3259-3270, (2008).
  • [2] Din, Q. and Elsayed, E.M., “Stability analysis of a discrete ecological model”, Computational Ecology and Software, 4(2): 89-103, (2014).
  • [3] Deeba, E., De Korvin, A. and Koh, E.L., “A fuzzy difference equation with an application”, Journal of Difference Equations and Applications, 2: 365-374, (1996).
  • [4] Deeba, E. and De Korvin, A., “Analysis by fuzzy difference equations of a model of level in blood”, Applied Mathematics Letters, 12: 33-40, (1999).
  • [5] Zhang, Q., Yang, L. and Liao, D., “On first-order fuzzy Ricatti difference equation”, Information Sciences, 270: 226-236, (2014).
  • [6] Zhang, Q., Liu, J. and Luo, Z., “Dynamical behavior of a third-order rational fuzzy difference equation”, Advances in Difference Equations, 2015(108): 18 pages, (2015).
  • [7] Rahman, G., Din, Q., Faizullah, F. and Khan, F.M., “Qualitative behavior of a second-order fuzzy difference equation”, Journal of Intelligent & Fuzzy Systems, 34: 745-753, (2018).
  • [8] Yalçınkaya, İ., Atak, N. and Tollu, D.T., “On a third-order fuzzy difference equation”, Journal of Prime Research in Mathematics, 17(1): 59-69, (2021).
  • [9] Hatir, E., Mansour, T. and Yalcinkaya, I., “On a fuzzy difference equation”, Utilitas Mathematica, 93: 135-151, (2014).
  • [10] Papaschinopoulos, G. and Papadopoulos, B. K., “On the fuzzy difference equation ”, Soft Computing, 6: 456-461, (2002).
  • [11] Stefanidou, G. and Papaschinopoulos, G., “A fuzzy difference equation of a rational form”, Journal of Nonlinear Mathematical Physics, 12: 300-315, (2005).
  • [12] Wang, C., Li, J. and Jia, L., “Dynamics of a high-order nonlinear fuzzy difference equations”, Journal of Applied Analysis & Computation, 11(1): 404-421, (2021).
  • [13] Atpinar, S. and Yazlik, Y., “Qualitative behavior of exponential type of fuzzy difference equations system”, Journal of Applied Mathematics and Computing, 69: 4135–4162 (2023).
  • [14] El-Owaidy, H.M., Ahmed, A.M. and Youssef, A.M., “The dynamics of the recursive sequence ”, Applied Mathematics Letters, 18(9): 1013-1018, (2005).
  • [15] Gümüş, M. and Soykan, Y., “Global character of a six-dimensional nonlinear system of difference equations”, Discrete Dynamics in Nature and Society, 2016, Article ID 6842521: 7 pages, (2016).
  • [16] Yalçınkaya, İ., Çalışkan, V. and Tollu, D.T., “On a nonlinear fuzzy difference equation”, Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 71(1): 68-78, (2022).
  • [17] Türk, G., Yalçınkaya, İ. and Tollu, D.T., “On solutions of a system of two fourth-order difference equations”, Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications & Algorithms, 25: 85-96, (2018).
  • [18] Bede, B., “Mathematics of Fuzzy Sets and Fuzzy Logic”, Springer, New York, 51-77, (2013).
  • [19] Wu, C. and Zhang, B., “Embedding problem of noncompact fuzzy number space ”, Fuzzy Sets and Systems, 105: 165-169, (1999).
  • [20] Klir, G. and Yuan, B., “Fuzzy Sets and Fuzzy Logic Theory and Applications”, Prentice Hall, New Jersey, 97-118, (1995).
  • [21] Papaschinopoulos, G. and Stefanidou, G., “Boundedness and asymptotic behavior of the solutions of a fuzzy difference equation”, Fuzzy Sets and Systems, 140: 523-539, (2003).

Yıl 2025, Cilt: 38 Sayı: 1, 275 - 290, 01.03.2025

İbrahim Yalçınkaya , Bilal Er , Durhasan Turgut Tollu

https://doi.org/10.35378/gujs.1098124

Öz

Kaynakça

  • [1] Chrysafis, K.A., Papadopoulos, B.K. and Papaschinopoulos, G., “On the fuzzy difference equations of finance”, Fuzzy Sets and Systems, 159: 3259-3270, (2008).
  • [2] Din, Q. and Elsayed, E.M., “Stability analysis of a discrete ecological model”, Computational Ecology and Software, 4(2): 89-103, (2014).
  • [3] Deeba, E., De Korvin, A. and Koh, E.L., “A fuzzy difference equation with an application”, Journal of Difference Equations and Applications, 2: 365-374, (1996).
  • [4] Deeba, E. and De Korvin, A., “Analysis by fuzzy difference equations of a model of level in blood”, Applied Mathematics Letters, 12: 33-40, (1999).
  • [5] Zhang, Q., Yang, L. and Liao, D., “On first-order fuzzy Ricatti difference equation”, Information Sciences, 270: 226-236, (2014).
  • [6] Zhang, Q., Liu, J. and Luo, Z., “Dynamical behavior of a third-order rational fuzzy difference equation”, Advances in Difference Equations, 2015(108): 18 pages, (2015).
  • [7] Rahman, G., Din, Q., Faizullah, F. and Khan, F.M., “Qualitative behavior of a second-order fuzzy difference equation”, Journal of Intelligent & Fuzzy Systems, 34: 745-753, (2018).
  • [8] Yalçınkaya, İ., Atak, N. and Tollu, D.T., “On a third-order fuzzy difference equation”, Journal of Prime Research in Mathematics, 17(1): 59-69, (2021).
  • [9] Hatir, E., Mansour, T. and Yalcinkaya, I., “On a fuzzy difference equation”, Utilitas Mathematica, 93: 135-151, (2014).
  • [10] Papaschinopoulos, G. and Papadopoulos, B. K., “On the fuzzy difference equation ”, Soft Computing, 6: 456-461, (2002).
  • [11] Stefanidou, G. and Papaschinopoulos, G., “A fuzzy difference equation of a rational form”, Journal of Nonlinear Mathematical Physics, 12: 300-315, (2005).
  • [12] Wang, C., Li, J. and Jia, L., “Dynamics of a high-order nonlinear fuzzy difference equations”, Journal of Applied Analysis & Computation, 11(1): 404-421, (2021).
  • [13] Atpinar, S. and Yazlik, Y., “Qualitative behavior of exponential type of fuzzy difference equations system”, Journal of Applied Mathematics and Computing, 69: 4135–4162 (2023).
  • [14] El-Owaidy, H.M., Ahmed, A.M. and Youssef, A.M., “The dynamics of the recursive sequence ”, Applied Mathematics Letters, 18(9): 1013-1018, (2005).
  • [15] Gümüş, M. and Soykan, Y., “Global character of a six-dimensional nonlinear system of difference equations”, Discrete Dynamics in Nature and Society, 2016, Article ID 6842521: 7 pages, (2016).
  • [16] Yalçınkaya, İ., Çalışkan, V. and Tollu, D.T., “On a nonlinear fuzzy difference equation”, Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 71(1): 68-78, (2022).
  • [17] Türk, G., Yalçınkaya, İ. and Tollu, D.T., “On solutions of a system of two fourth-order difference equations”, Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications & Algorithms, 25: 85-96, (2018).
  • [18] Bede, B., “Mathematics of Fuzzy Sets and Fuzzy Logic”, Springer, New York, 51-77, (2013).
  • [19] Wu, C. and Zhang, B., “Embedding problem of noncompact fuzzy number space ”, Fuzzy Sets and Systems, 105: 165-169, (1999).
  • [20] Klir, G. and Yuan, B., “Fuzzy Sets and Fuzzy Logic Theory and Applications”, Prentice Hall, New Jersey, 97-118, (1995).
  • [21] Papaschinopoulos, G. and Stefanidou, G., “Boundedness and asymptotic behavior of the solutions of a fuzzy difference equation”, Fuzzy Sets and Systems, 140: 523-539, (2003).
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Mathematics
Yazarlar

İbrahim Yalçınkaya 0000-0003-4546-4493

Bilal Er 0000-0003-2461-3330

Durhasan Turgut Tollu 0000-0002-3313-8829

Erken Görünüm Tarihi 3 Ocak 2025
Yayımlanma Tarihi 1 Mart 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 38 Sayı: 1

Kaynak Göster

APA Yalçınkaya, İ., Er, B., & Tollu, D. T. (2025). Dynamic Behavior of a Fourth-Order Nonlinear Fuzzy Difference Equation. Gazi University Journal of Science, 38(1), 275-290. https://doi.org/10.35378/gujs.1098124
AMA Yalçınkaya İ, Er B, Tollu DT. Dynamic Behavior of a Fourth-Order Nonlinear Fuzzy Difference Equation. Gazi University Journal of Science. Mart 2025;38(1):275-290. doi:10.35378/gujs.1098124
Chicago Yalçınkaya, İbrahim, Bilal Er, ve Durhasan Turgut Tollu. “Dynamic Behavior of a Fourth-Order Nonlinear Fuzzy Difference Equation”. Gazi University Journal of Science 38, sy. 1 (Mart 2025): 275-90. https://doi.org/10.35378/gujs.1098124.
EndNote Yalçınkaya İ, Er B, Tollu DT (01 Mart 2025) Dynamic Behavior of a Fourth-Order Nonlinear Fuzzy Difference Equation. Gazi University Journal of Science 38 1 275–290.
IEEE İ. Yalçınkaya, B. Er, ve D. T. Tollu, “Dynamic Behavior of a Fourth-Order Nonlinear Fuzzy Difference Equation”, Gazi University Journal of Science, c. 38, sy. 1, ss. 275–290, 2025, doi: 10.35378/gujs.1098124.
ISNAD Yalçınkaya, İbrahim vd. “Dynamic Behavior of a Fourth-Order Nonlinear Fuzzy Difference Equation”. Gazi University Journal of Science 38/1 (Mart 2025), 275-290. https://doi.org/10.35378/gujs.1098124.
JAMA Yalçınkaya İ, Er B, Tollu DT. Dynamic Behavior of a Fourth-Order Nonlinear Fuzzy Difference Equation. Gazi University Journal of Science. 2025;38:275–290.
MLA Yalçınkaya, İbrahim vd. “Dynamic Behavior of a Fourth-Order Nonlinear Fuzzy Difference Equation”. Gazi University Journal of Science, c. 38, sy. 1, 2025, ss. 275-90, doi:10.35378/gujs.1098124.
Vancouver Yalçınkaya İ, Er B, Tollu DT. Dynamic Behavior of a Fourth-Order Nonlinear Fuzzy Difference Equation. Gazi University Journal of Science. 2025;38(1):275-90.