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Qualitative behavior of exponential type of fuzzy difference equations system

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Abstract

In this paper, we study the existence, uniqueness, and qualitative behavior of the fuzzy positive solutions to the following exponential type non-linear system of fuzzy difference equations with second-order.

$$\begin{aligned} x_{n+1}=\frac{\alpha _{1}+\beta _{1}e^{-x_{n-1}}}{\gamma _{1}+y_{n}},&\quad y_{n+1}=\frac{\alpha _{2}+\beta _{2}e^{-y_{n-1}}}{\gamma _{2}+x_{n}}, \quad n\in {\mathbb {N}}_{0}, \end{aligned}$$

where \(\alpha _{1},\alpha _{2}, \beta _{1},\beta _{2}, \gamma _{1}, \gamma _{2}\) are positive fuzzy numbers with the \(x_{-i},y_{-i},i \in \{0,1\},\) the fuzzy initial conditions. Also we give some numerical applications to support the theoretical aspects of the results.

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  1. Mathematics Department, Nevsehir Haci Bektas Veli University, Nevşehir, Turkey

    Sevda Atpinar & Yasin Yazlik

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  1. Sevda Atpinar
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Atpinar, S., Yazlik, Y. Qualitative behavior of exponential type of fuzzy difference equations system. J. Appl. Math. Comput. 69, 4135–4162 (2023). https://doi.org/10.1007/s12190-023-01919-y

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