Dynamic analysis of high-order fuzzy difference equation

In the present paper, we discuss the existence, boundedness, and asymptotic behavior of the positive solutions of the fuzzy difference equation \(\begin{aligned} \omega _{n+1}=\frac{A\omega _{n-1}}{B+C\omega _{n-k}^{p}},\quad n\in \mathbb { N}_{0} \end{aligned}\) $$\begin{array}{c}\hfill {\omega }_{n+1}=\frac{A{\omega }_{n-1}}{B+C{\omega }_{n-k}^p},n\in {\mathbb{N}}_0\end{array}$$ with the parameters A, B, C and the initial conditions \(\omega _{-i}\) ${\omega }_{-i}$ \( (i=0,1,...,k)\ \) $(i=0,1,...,k)$ are positive fuzzy numbers and \(p,k\in \mathbb {{\mathbb {Z}}} ^{+}.\) $p,k\in {\mathbb{Z}}^{+}.$ The theoretical results obtained are also supported and visualized by numerical simulations.