In this paper we investigate the existence, the boundedness and the asymptotic behavior of the positive solutions of the fuzzy difference equation \[z_{n+1}=\dfrac{Az_{n-1}}{1+z_{n-2}^{p}},~n\in\mathbb{N}_{0}\] where ( z n ) (zn) is a sequence of positive fuzzy numbers, A A and the initial conditions z − j z−j ( j = 0 , 1 , 2 ) (j=0,1,2) are positive fuzzy numbers and p p is a positive integer.
📌 3 Maddede Bu Makale
🎯
Amaç & Hipotez:In this paper we investigate the existence, the boundedness and the asymptotic behavior of the positive solutions of the fuzzy difference equation \[z_{n+1}=\dfrac{Az_{n-1}}{1+z_{n-2}^{p}},~n\in\mathbb{N}_{0}\] where ( z n ) (zn) is a sequence of positive fuzzy numbers, A A and the initial conditions z − j z−j ( j = 0 , 1 , 2 ) (j=0,1,2) are positive fuzzy numbers and p p is a positive integer.
📊
Temel Bulgular & Veri:In this paper we investigate the existence, the boundedness and the asymptotic behavior of the positive solutions of the fuzzy difference equation \[z_{n+1}=\dfrac{Az_{n-1}}{1+z_{n-2}^{p}},~n\in\mathbb{N}_{0}\] where ( z n ) (zn) is a sequence of positive fuzzy numbers, A A and the initial conditions z − j z−j ( j = 0 , 1 , 2 ) (j=0,1,2) are positive fuzzy numbers and p p is a positive integer.
💡
Sonuç & Katkı:In this paper we investigate the existence, the boundedness and the asymptotic behavior of the positive solutions of the fuzzy difference equation \[z_{n+1}=\dfrac{Az_{n-1}}{1+z_{n-2}^{p}},~n\in\mathbb{N}_{0}\] where ( z n ) (zn) is a sequence of positive fuzzy numbers, A A and the initial conditions z − j z−j ( j = 0 , 1 , 2 ) (j=0,1,2) are positive fuzzy numbers and p p is a positive integer.
In this paper we investigate the existence, the boundedness and the asymptotic behavior of the positive solutions of the fuzzy difference equation \[z_{n+1}=\dfrac{Az_{n-1}}{1+z_{n-2}^{p}},~n\in\mathbb{N}_{0}\] where ( z n ) (zn) is a sequence of positive fuzzy numbers, A A and the initial conditions z − j z−j ( j = 0 , 1 , 2 ) (j=0,1,2) are positive fuzzy numbers and p p is a positive integer.
Yalçınkaya, İ., Çalışkan, V., Tollu, D. T. (2022). On a nonlinear fuzzy difference equation. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 71 Issue: 1. https://doi.org/10.31801/cfsuasmas.861915
Bede, B., Mathematics of Fuzzy Sets and Fuzzy Logic, Springer, New York, 2013.
Chrysafis, K. A., Papadopoulos, B. K., Papaschinopoulos, G., On the fuzzy difference equations of finance, Fuzzy Sets Syst., 159 (2008), 3259–3270. https://doi:10.1016/j.fss.2008.06.007
Deeba, E., De Korvin, A., Koh, E. L., A fuzzy difference equation with an application, J. Differ. Equ. Appl., 2 (1996), 365–374. https://doi.org/10.1080/10236199608808071
Deeba, E., De Korvin, A., Analysis by fuzzy difference equations of a model of CO2 level in blood, Appl. Math. Lett., 12 (1999), 33–40. https://doi.org/10.1016/S0893-9659(98)00168-2
El-Owaidy, H. M., Ahmed, A. M., Youssef, A. M., The dynamics of the recursive sequence $x_{n+1}=(\alpha x_{n-1})/(\beta +\gamma x_{n-2}^{p})$, Appl. Math. Lett., 18(9) (2005), 1013-1018. https://doi.org/10.1016/j.aml.2003.09.014
Elsayed, E. M., On the solutions and periodic nature of some systems of difference equations, Int. J. Biomath., 7 (2014), 26 pages. https://doi.org/10.1142/S1793524514500673
Gumus, M., Soykan, Y., Global character of a six-dimensional nonlinear system of difference equations, Discrete Dyn. Nat. Soc., Article ID 6842521 (2016), 7 pages. https://doi.org/10.1155/2016/6842521
Klir, G., Yuan, B., Fuzzy Sets and Fuzzy Logic Theory and Applications, Prentice Hall, New Jersey, 1995.
Hatir, E., Mansour, T., Yalcinkaya, I., On a fuzzy difference equation, Util. Math., 93 (2014), 135-151.
Negoita, C. V., Ralescu, D., Applications of Fuzzy Sets to Systems Analysis, Birkhauser, Verlag, Besel, 1975.
Papaschinopoulos, G., Papadopoulos, B. K., On the fuzzy difference equation $x_{n+1}=A+B/x_{n}$, Soft Comput., 6 (2002), 456-461. https://doi.org/10.1007/s00500-001-0161-7
Papaschinopoulos, G., Papadopoulos, B. K., On the fuzzy difference equation $x_{n+1}=A+x_{n}/x_{n-m}$, Fuzzy Sets Syst., 129 (2002), 73-81. https://doi.org/10.1016/S0165- 0114(01)00198-1
Stefanidou, G., Papaschinopoulos, G., A fuzzy difference equation of a rational form, J. Nonlinear Math. Phys., 12 (2005), 300–315. https://doi.org/10.2991/jnmp.2005.12.s2.21
Pielou, E. C., Population and Community Ecology: Principles and Methods, CRC Press, London, 1974.
Popov, E. P., Automatic Regulation and Control, (Russian) Nauka, Moscow, 1966.